Research Seminar Numerical Analysis

Wed, 17.07.24 at 13:15

2.417

Stefan Sauter Uni Zürich

The acoustic half space Green's function with impedance boundary condition in d spatial dimensions: Fast evaluation and numerical quadrature

Abstract.

In our talk, we introduce a representation of the acoustic half space Green's function with impedance boundary conditions in d space dimensions which avoids oscillatory Fourier integrals. A numerical quadrature method is developed for its fast evaluation. In the context of boundary element methods this function must be integrated over pairs of simplices and we present an efficient approximation method.

Numerical Analysis

Wed, 10.07.24 at 13:15

2.417

Lara Theallier HU Berlin

Lower energy bounds in the Landau-de Gennes model for nematic liquid crystals

Numerical Analysis

Wed, 03.07.24 at 13:15

2.417

Ngoc Tien Tran Uni Augsburg

Hybrid high-order method for the biharmonic eigenvalue problem

Numerical Analysis

Mon, 01.07.24 at 13:15

2.417

Norbert Heuer PUC Chile

Abstrakte hybride Galerkin Methoden

Numerical Analysis

Wed, 19.06.24 at 13:15

2.417

Tim Stiebert HU Berlin

Guaranteed lower eigenvalue bounds for the Schrödinger eigenvalue problem

Numerical Analysis

Wed, 05.06.24 at 13:15

2.417

Stefan Sauter Uni Zürich

The acoustic half space Green's function with impedance boundary condition in d spatial dimensions: Fast evaluation and numerical quadrature

Abstract.

In our talk, we introduce a representation of the acoustic half space Green's function with impedance boundary conditions in d space dimensions which avoids oscillatory Fourier integrals. A numerical quadrature method is developed for its fast evaluation. In the context of boundary element methods this function must be integrated over pairs of simplices and we present an efficient approximation method.

Numerical Analysis

Wed, 05.06.24 at 13:15

2.417

Benedikt Gräßle HU Berlin

Analysing WOPSIP by supercloseness

Numerical Analysis

Wed, 29.05.24 at 13:15

2.006

Carsten Carstensen HU Berlin

A simple approach for companion operators for Crouzeix-Raviart finite element spaces with inhomogeneous Dirichlet boundary conditions

Numerical Analysis

Wed, 22.05.24 at 13:15

2.417

Ruma Maity Uni Innsbruck

Finite element methods for the Landau-de Gennes minimization problem of nematic liquid crystals

Abstract.

Nematic liquid crystals represent a transitional state of matter between liquid and crystalline phases that combine the fluidity of liquids with the ordered structure of crystalline solids. These materials are widely utilized in various practical applications, such as display devices, sensors, thermometers, nanoparticle organizations, proteins, and cell membranes. In this talk, we discuss finite element approximation of the nonlinear elliptic partial differential equations associated with the Landau-de Gennes model for nematic liquid crystals. We establish the existence and local uniqueness of the discrete solutions, a priori error estimates, and a posteriori error estimates that steer the adaptive refinement process. Additionally, we explore Ball and Majumdar's modifications of the Landau-de Gennes Q-tensor model that enforces the physically realistic values of the Q tensor eigenvalues. We discuss some numerical experiments that corroborate the theoretical estimates, and adaptive mesh refinements that capture the defect points in nematic profiles.

Numerical Analysis

Mon, 13.05.24 at 15:15

2.417

Asha Dond IISER TVM

Quasi-optimality of adaptive FEMs for distributed elliptic optimal control problems

Abstract.

In this talk, we will discuss the quasi-optimality of adaptive nonconform- ing finite element methods for distributed optimal control problems governed by m-harmonic operators for m = 1, 2. A variational discretization approach is employed and the state and adjoint variables are discretized using non- conforming finite elements. The general axiomatic framework that includes stability, reduction, discrete reliability, and quasi-orthogonality establishes the quasi-optimality. Numerical results demonstrate the theoretically pre- dicted orders of convergence.

Numerical Analysis

Wed, 08.05.24 at 13:15

2.417

Benedikt Gräßle HU Berlin

Inf-sup bounds for semilinear problems from nonconforming discretisations

Numerical Analysis

Wed, 24.04.24 at 13:15

2.417

Christian Merdon WIAS Berlin

Pressure-robustness in Navier-Stokes simulations

Numerical Analysis

Wed, 17.04.24 at 15:15

2.417

Tim Stiebert HU Berlin

Guaranteed lower eigenvalue bounds via a conforming FEM

Numerical Analysis

Wed, 17.04.24 at 13:15

2.417

Carsten Carstensen HU Berlin

Discussion on duality in the Poisson model problem

Numerical Analysis

Fri, 08.12.23 at 13:15

3.006

Carsten Carstensen HU Berlin

Hs(Ω) for 0<s<1 (Fortsetzung)

Numerical Analysis

Tue, 05.12.23 at 11:15

2.417

Johannes Storn Universität Bielefeld

Adaptive Mesh Refinement for arbitrary initial Triangulations

Abstract.

This talk introduces a simple initialization of the Maubach/Traxler bisection routine for adaptive mesh refinements. This initialization applies to any conforming initial triangulation. It preserves shape-regularity, satisfies the closure estimate needed for optimal convergence of adaptive schemes, and allows for the intrinsic use of existing implementations. This talk results from joint work with Lars Diening (Bielefeld University) and Lukas Gehring (Friedrich-Schiller-Universität Jena).

Numerical Analysis

Fri, 01.12.23 at 10:00

3.008

Carsten Carstensen HU Berlin

Hs(Ω) for 0<s<1

Numerical Analysis

Tue, 28.11.23 at 11:15

2.417

Julia Schaeffer HU Berlin

Contour integration methods for nonlinear eigenvalue problems in nanooptics

Numerical Analysis

Thu, 23.11.23 at 11:15

2.417

Quanling Deng Australian National University

Particle-Continuum Multiscale Modeling of Sea Ice Floes

Abstract.

In this talk, I will start by presenting some quick facts about Arctic and Antarctic sea ice floes followed by a quick overview of the major sea ice continuum and particle models. I will then present our main contribution to its multiscale modelling. The recent Lagrangian particle model based on the discrete element method (DEM) has shown improved model performance and started to gain more attention from groups that are working on Global Climate Models (GCMs). We adopt the DEM model for sea ice dynamical simulation. The major challenges are 1) model coupling in different frames of reference (Lagrangian for sea ice while Eulerian for the ocean and atmosphere dynamics); 2) the heavy computational cost when the number of the floes is large; and 3) inaccurate floe parameterisation when the floe distribution has multiscale features. To overcome these challenges, I will present a superfloe parameterisation to reduce the computational cost and a superparameterisation method to capture the multiscale features. In particular, the superfloe parameterisation facilitates noise inflation in data assimilation that recovers the unobserved ocean field underneath the sea ice. To capture the multiscale features, we adopt the Boltzmann equation for particles and superparameterise the sea ice floes as continuity equations governing the statistical moments. This leads to a particle-continuum coupled multiscale model. I will present several numerical experiments to demonstrate the success of the proposed method. This is joint work with Sam Stechmann (UW-Madison) and Nan Chen (UW-Madison).

Numerical Analysis

Wed, 22.11.23 at 11:15

2.417

Lara Theallier HU Berlin

Hybrid-high-order methods for linear elasticity

Numerical Analysis

Tue, 21.11.23 at 11:15

2.417

Georgi Mitsov HU Berlin

Time-space variational formulations for the heat equation

Numerical Analysis

Mon, 13.11.23 at 16:00

2.417

Neela Nataraj IIT Bombay

Adaptive Computation of Fourth-Order Problems

Numerical Analysis

Mon, 13.11.23 at 11:00

2.417

Norbert Heuer Pontificia Universidad Católica de Chile

Normal-normal continuous symmetric stresses in finite element elasticity

Numerical Analysis

Tue, 07.11.23 at 11:15

2.417

Sophie Puttkammer HU Berlin

Notes on Morley FEM in 3D

Numerical Analysis

Wed, 01.11.23 at 11:15

2.417

Tien Tran Ngoc Universität Augsburg

Lower eigenvalue bounds with hybrid high-order methods

Numerical Analysis

Tue, 31.10.23 at 11:15

2.417

Benedikt Gräßle HU Berlin

On nonconforming approximations for a class of semilinear problems

Numerical Analysis

Thu, 26.10.23 at 11:15

online

Felix Goldmann HU Berlin

Unstetige Galerkinverfahren für das parabolische Hindernisproblem

Numerical Analysis

Tue, 24.10.23 at 11:15

2.417

Sophie Puttkammer HU Berlin

An enriched Crouzeix-Raviart FEM for guaranteed lower eigenvalue bounds

Numerical Analysis

Tue, 17.10.23 at 13:15

2.417

Christian Merdon WIAS Berlin

Gradient-robust hybrid discontinuous Galerkin discretizations for the compressible Stokes equations

Abstract.

The talk introduces the concept of gradient-robustness for the velocity-density formulation of the compressible Stokes and its connection to the preservation of certain well-balanced states. Gradient-robust hybrid discontinuous Galerkin (HDG) discretisations of arbitrary order are discussed. The lowest-order scheme is shown to be non-negativity preserving and, at least in the isothermal case with linear equation of state, to be stable and provably convergent. The gradient-robustness property dramatically enhances the accuracy in well-balanced situations, such as the hydrostatic balance where the pressure gradient balances the gravity force, but also in non-hydrostatic cases for low Mach numbers and small viscosities. This is demonstrated in some numerical examples. (joint work with Philip Lederer)

Numerical Analysis

Tue, 11.07.23 at 15:15

2.417

Norbert Heuer PUC Chile

Conforming Galerkin schemes via traces and applications to plate bending -- Teil 2

Numerical Analysis

Fri, 07.07.23 at 12:15

Uni Leipzig

Benedikt Gräßle HU Berlin

Stabilization-free a posteriori error analysis for hybrid-high order methods

Numerical Analysis

Fri, 07.07.23 at 10:45

Uni Leipzig

Jonas Ketteler Uni Leipzig

Some ideas for the quasi-orthogonality for the Fortin-Soulie FEM

Numerical Analysis

Fri, 07.07.23 at 09:15

Uni Leipzig

Lara Theallier HU Berlin

HHO for linear elasticity

Numerical Analysis

Thu, 06.07.23 at 16:45

Uni Leipzig

Carsten Carstensen HU Berlin

Lower eigenvalue bounds of the Laplacian

Numerical Analysis

Thu, 06.07.23 at 15:15

Uni Leipzig

Mira Schedensack Uni Leipzig

Discrete Helmholtz decompositions

Numerical Analysis

Tue, 20.06.23 at 13:15

2.417

Benedikt Gräßle HU Berlin

The pressure-wired Stokes element

Abstract.

The conforming Scott-Vogelius pair for the stationary Stokes equation in 2D is a popular finite element which is inf-sup stable for any fixed regular triangulation. However, the inf-sup constant deteriorates if the "singular distance" (measured by some geometric mesh quantity Θₘᵢₙ > 0) of the finite element mesh to certain "singular" mesh configurations is small. In this paper we present a modification of the classical Scott-Vogelius element of arbitrary polynomial order k ≥ 4 for the velocity where a constraint on the pressure space is imposed if locally the singular distance is smaller than some control parameter η > 0. We establish a lower bound on the inf-sup constant in terms of Θₘᵢₙ+η > 0 independent of the maximal mesh width and the polynomial degree that does not deteriorate for small Θₘᵢₙ≪1. The divergence of the discrete velocity is at most of size O(η) and very small in practical examples. In the limit η→0 we recover and improve estimates for the classical Scott-Vogelius Stokes element. This talk presents joint work with Nis-Erik Bohne and Stefan Sauter, University of Zurich.

Numerical Analysis

Tue, 13.06.23 at 13:15

2.417

Emilie Pirch Uni Jena

Guaranteed lower eigenvalue bounds with three skeletal methods

Numerical Analysis

Tue, 06.06.23 at 13:15

2.006

Carsten Carstensen HU Berlin

Smoother

Numerical Analysis

Tue, 30.05.23 at 13:15

2.417

Joscha Gedicke Uni Bonn

P₁ finite element methods for an elliptic optimal control problem with pointwise state constraints

Abstract.

We present theoretical and numerical results for two P₁ finite element methods for an elliptic distributed optimal control problem on general polygonal/polyhedral domains with pointwise state constraints.

Numerical Analysis

Tue, 23.05.23 at 13:15

2.417

Johannes Storn Uni Bielefeld

Advantages of Dual Formulations in Computational Calculus of Variations

Abstract.

Duality theory is a very useful tool in the calculus of variations. In this talk we exploit this tool to overcome the Lavrentiev gap phenomenon and to design an iterative scheme for the computation of the p-Laplace problem with large exponents.

Numerical Analysis

Tue, 16.05.23 at 15:00

2.417

Ngoc Tien Tran Uni Jena

Minimal residual methods for PDE of second order in nondivergence form

Numerical Analysis

Tue, 16.05.23 at 13:15

2.417

Felix Goldmann HU Berlin

Discontinuous Galerkin method for the Parabolic Obstacle Problem

Numerical Analysis

Wed, 10.05.23 at 14:45

2.417

Neela Nataraj IIT Bombay

Discussion on WOPSIP

Numerical Analysis

Tue, 09.05.23 at 13:15

2.417

Lara Theallier HU Berlin

Implementing HHO for linear elasticity

Numerical Analysis

Tue, 02.05.23 at 13:15

2.417

Stefan Sauter Uni Zürich

The method of integral equations for acoustic transmission problems with varying coefficients

Abstract.

In our talk we will derive an integral equation method which transforms a three-dimensional acoustic transmission problem with variable coefficients and mixed boundary conditions to a non-local equation on the two-dimensional boundary and skeleton of the domain. For this goal, we introduce and analyze abstract layer potentials as solutions of auxiliary coercive full space variational problems and derive jump conditions across domain interfaces. This allows us to formulate the non-local skeleton equation as a direct method for the unknown Cauchy data of the original partial differential equation. We develop a theory which inherits coercivity and continuity of the auxiliary full space variational problem to the resulting variational form of the skeleton equation without relying on an explicit knowledge of Green's function. Some concrete examples of full and half space transmission problems with piecewise constant coefficients are presented which illustrate the generality of our integral equation method and its theory. This talk comprises joint work with Francesco Florian, University of Zurich and Ralf Hiptmair, ETH Zurich.

Numerical Analysis

Tue, 25.04.23 at 13:15

2.417

Georgi Mitsov HU Berlin

Combining time-stepping θ-schemes with dPG-FEM for the solution of the heat equation

Numerical Analysis

Wed, 19.04.23 at 13:15

2.417

Benedikt Gräßle HU Berlin

The hierarchical Argyris AFEM with optimal convergence rates

Numerical Analysis

Tue, 29.11.22 at 11:15

1.410

Michael Feischl TU Wien

Local equivalence of residuals in random PDEs

Numerical Analysis

Thu, 27.10.22 at 09:15

2.417

Felix Goldmann HU Berlin

Discontinuous Galerkin method for the parabolic obstacle problem with a functional a posteriori error estimator

Numerical Analysis

Thu, 20.10.22 at 09:15

2.417

Philipp Bringmann HU Berlin

A (hybrid) discontinuous least-squares finite element method with built-in a posteriori error estimation

Numerical Analysis

Wed, 15.07.20 at 17:15

online

Tien Tran-Ngoc HU Berlin

GPU computing in MATLAB for a higher-order method

Numerical Analysis

Wed, 08.07.20 at 17:15

online

Georgi Mitsov HU Berlin

Elements of stability analysis for the heat equation

Numerical Analysis

Wed, 01.07.20 at 17:15

online

Emilie Pirch HU Berlin

Introduction and implementation of an HHO method

Numerical Analysis

Wed, 24.06.20 at 17:15

online

Julian Streitberger HU Berlin

C0 interior penalty methods for the biharmonic problem

Numerical Analysis

Wed, 17.06.20 at 17:15

online

Henrik Schneider HU Berlin

DPG for Laplace eigenvalue problem

Numerical Analysis

Wed, 10.06.20 at 18:00

online

Carsten Carstensen HU Berlin

Introduction to dG4plates

Numerical Analysis

Wed, 10.06.20 at 17:15

online

Tien Tran-Ngoc HU Berlin

Unstabilized Hybrid High-Order method for a class of degenerate convex minimization problems

Numerical Analysis

Wed, 03.06.20 at 17:15

online

Philipp Bringmann HU Berlin

Towards an efficient implementation of newest-vertex bisection with separate marking in MATLAB

Numerical Analysis

Wed, 27.05.20 at 17:15

online

Johannes Storn Universität Bielefeld

On the Sobolev and Lp stability of the L² projection

Numerical Analysis

Wed, 20.05.20 at 17:15

online

Jörn Wichmann Universität Bielefeld

The parabolic p-Laplacian with fractional differentiability

Abstract.

We study the parabolic p-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space-time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskii spaces and therefore cover situations when the (gradient of) the solution has only fractional derivatives in space and time. The main novelty is that, different to all previous results, we do not assume any coupling condition between the space and time resolution h and τ. The theoretical error analysis is complemented by numerical experiments. This is joint work with Dominic Breit, Lars Diening, and Johannes Storn.

Numerical Analysis

Wed, 13.05.20 at 17:15

online

Sophie Puttkammer HU Berlin

Notes on Morley in 3D

Numerical Analysis

Wed, 06.05.20 at 17:00

online

Carsten Carstensen HU Berlin

Abstract nonconforming schemes

Numerical Analysis

Wed, 29.04.20 at 09:15

online

Rui Ma Universität Duisburg Essen

Adaptive least-squares finite element methods for non-selfadjoint indefinite second-order linear elliptic problems

Abstract.

In this talk we establish the convergence of adaptive least-squares finite element methods for second-order linear non-selfadjoint indefinite elliptic problems in three dimensions. The error is measured in the L² norm of the flux variable and then allows for an adaptive algorithm with collective marking. The axioms of adaptivity apply to this setting and guarantee the rate optimality for sufficiently small initial mesh-sizes and bulk parameter.

Numerical Analysis

Mon, 20.04.20 at 11:15

online

Fleurienne Bertrand HU Berlin

First order least-squares formulations for eigenvalue problems

Abstract.

In this talk we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the corresponding continuous eigenmodes is studied and analyzed with the help of appropriate L² error estimates. A priori and a posteriori estimates are proved. This is joint work with Daniele Boffi.

Numerical Analysis

Wed, 12.02.20 at 11:15

TBA

Joscha Matysiak HU Berlin

Numerical Analysis

Fri, 31.01.20 at 13:30

2.417

Philipp Bringmann HU Berlin

Adaptive least-squares finite element method with optimal convergence rates

Numerical Analysis

Wed, 29.01.20 at 16:15

2.417

Alexander Heinlein Universität zu Köln

Overlapping Schwarz preconditioning techniques for nonlinear problems

Numerical Analysis

Wed, 29.01.20 at 11:15

3.007

Georgi Mitsov HU Berlin

Well-posedness of generalized dPG methods with locally weighted test-search norms for the heat equation

Numerical Analysis

Wed, 22.01.20 at 11:15

Joscha Matysiak HU Berlin

This presentation is rescheduled on February 12th.

Numerical Analysis

Wed, 15.01.20 at 11:15

2.417

Philipp Bringmann HU Berlin

Convergence proofs for adaptive LSFEMs and implementation of the octAFEM3D software package

Numerical Analysis

Fri, 10.01.20 at 13:00

3.008

Oliver Sander TU Dresden

Geometric Finite Element

Numerical Analysis

Wed, 08.01.20 at 11:15

2.417

Sophie Puttkammer HU Berlin

Remarks on optimal convergence rates for guaranteed lower eigenvalue bounds with a modified nonconforming method

Numerical Analysis

Wed, 18.12.19 at 11:00

2.417

Henrik Schneider HU Berlin

DPG for the Laplace eigenvalue problem

Numerical Analysis

Wed, 11.12.19 at 11:15

2.417

Benedikt Gräßle HU Berlin

Numerical Analysis with HHO methods

Numerical Analysis

Wed, 04.12.19 at 11:15

2.417

Céline Torres Universität Zürich

Stability of the Helmholtz equation with highly oscillatory coefficients

Abstract.

Existence and uniqueness of the heterogeneous Helmholtz problem on bounded domains can be shown using a unique continuation principle in Fredholm's alternative. This results in an energy estimate of the problem, with a stability constant that is not directly explicit in the coefficients or the wave number. We show, that for highly oscillatory coefficients, the solution can exhibit a localised wave. As a result the stability grows exponentially in the wave number. We discuss how this constant enters in the condition for quasi-optimality, when using a hp-Finite Element Method to discretise the problem and the difficulties that arise therein.

Numerical Analysis

Wed, 27.11.19 at 15:00

2.417

Stefan Sauter Universität Zürich

𝒟ℋ2 Matrices and their Application to Scattering Problems

Abstract.

The sparse approximation of high-frequency Helmholtz-type integral operators has many important physical applications such as problems in wave propagation and wave scattering. The discrete system matrices are huge and densely populated; hence their sparse approximation is of outstanding importance. In our talk we will generalize the directional ℋ2 -matrix techniques from the "pure" Helmholtz operator Lu=−Δu+z2u with z=−ik;k real, to general complex frequencies z with Re(z)>0. In this case, the fundamental solution decreases exponentially for large arguments. We will develop a new admissibility condition which contain Re(z) and Im(z) in an explicit way and introduce the approximation of the integral kernel function on admissible blocks in terms of frequency-dependent directional expansion functions. We present an error analysis which is explicit with respect to the expansion order and with respect to the real and imaginary part of z. This allows us to choose the variable expansion order in a quasi-optimal way depending on Re(z) but independent of, possibly large, Im(z). The complexity analysis is explicit with respect to Re(z) and Im(z) and shows how higher values of Re(z) reduce the complexity. In certain cases, it even turns out that the discrete matrix can be replaced by its nearfield part. Numerical experiments illustrate the sharpness of the derived estimates and the efficiency of our sparse approximation. This talk comprises joint work with S. Börm, Christian-Albrechts-Universität Kiel, Germany and M. Lopez-Fernandez, Sapienza Universita di Roma, Italy.

Numerical Analysis

Wed, 20.11.19 at 11:15

2.417

Ma Rui HU Berlin

Convergence of the adaptive nonconforming element method for an obstacle problem

Numerical Analysis

Wed, 13.11.19 at 11:15

2.417

Ornela Mulita SISSA

Smoothed Adaptive Finite Element Methods

Abstract.

We propose a new algorithm for Adaptive Finite Element Methods based on Smoothing iterations (S-AFEM). The algorithm is inspired by the ascending phase of the V-cycle multigrid method: we replace accurate algebraic solutions in intermediate cycles of the classical AFEM with the application of a prolongation step, followed by a fixed number of few smoothing steps. The method reduces the overall computational cost of AFEM by providing a fast procedure for the construction of a quasi-optimal mesh sequence with large algebraic error in the intermediate cycles. Indeed, even though the intermediate solutions are far from the exact algebraic solutions, we show that their a-posteriori error estimation produces a refinement pattern that is substantially equivalent to the one that would be generated by classical AFEM, at a considerable fraction of the computational cost. In this talk, we will quantify rigorously how the error propagates throughout the algorithm, and then we will provide a connection with classical a posteriori error analysis. Finally, we will present a series of numerical experiments that highlights the efficiency and the computational speedup of S-AFEM.

Numerical Analysis

Wed, 06.11.19 at 14:45

2.417

Neela Nataraj IIT Bombay

Finite element methods for nematic liquid crystals

Abstract.

We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element methods are used to approximate the solutions of this nonlinear problem with non-homogeneous Dirichlet boundary conditions. A discrete inf-sup condition demonstrates the stability of the discontinuous Galerkin discretization of a well-posed linear problem. We then establish the existence and local uniqueness of the discrete solution of the non-linear problem. An a priori error estimate in the energy norm is derived and the quadratic convergence of Newton’s iterates is illustrated. This is a joint work with Ruma Maity and Apala Majumdar.

Numerical Analysis

Wed, 06.11.19 at 11:15

2.417

Julia Schaeffer HU Berlin

Convergence rates for the FEAST algorithm with dPG resolvent discretization

Numerical Analysis

Thu, 31.10.19 at 09:30

2.417

Max Gunzburger Florida State University

Integral equation modeling for anomalous diffusion and nonlocal mechanics

Abstract.

We use the canonical examples of fractional Laplacian and peridynamics equations to discuss their use as models for nonlocal diffusion and mechanics, respectively, via integral equations with singular kernels. We then proceed to discuss theories for the analysis and numerical analysis of the models considered, relying on a nonlocal vector calculus to define weak formulations in function space settings. In particular, we discuss the recently developed asymptotically compatible families of discretization schemes. Brief forays into examples and extensions are made, including obstacle problems and wave problems.

Numerical Analysis

Wed, 30.10.19 at 11:15

3.007

Tien Tran-Ngoc HU Berlin

HHO methods for a class of degenerate convex minimization problems

Numerical Analysis

Tue, 29.10.19 at 11:15

2.417

Tim Ricken Universität Stuttgart

Neue Methoden zur Modellierung von Mehrphasenmaterialien mit Mehrskalenansätzen - Anwendungsbeispiele aus den Bereichen Materialwissenschaft, Biomechanik und Umwelttechnik

Numerical Analysis

Wed, 23.10.19 at 11:45

2.417

Sophie Puttkammer HU Berlin

A modified HHO method to compute guaranteed lower eigenvalue bounds

Numerical Analysis

Wed, 23.10.19 at 11:15

2.417

Julian Streitberger HU Berlin

Two Lowest Order MFEM Examples

Numerical Analysis

Wed, 16.10.19 at 11:15

3.007

Georgi Mitsov HU Berlin

On the well-posedness of a generalized dPG time-stepping methods for the heat equation

Numerical Analysis

Thu, 11.07.19 at 16:00

2.417

Amiya Pani IIT Bombay

On Fractional in Time Evolution Problems: Some Theoretical and Computational Studies

Numerical Analysis

Wed, 10.07.19 at 09:15

2.417

Julia Schaeffer HU Berlin

FEAST spectral approximation using dPG resolvent discretization

Numerical Analysis

Fri, 05.07.19 at 09:15

2.417

Johannes Storn HU Berlin

Topics in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Analysis

Abstract.

The first part of this thesis defense explores the accuracy of solutions to the LSFEM. It combines properties of the underlying partial differential equation with properties of the LSFEM and so proves the asymptotic equality of the error and a computable residual. Moreover, this talk introduces an novel scheme for the computation of guaranteed upper error bounds. While the established error estimator leads to a significant overestimation of the error, numerical experiments indicate a tiny overestimation with the novel bound. The investigation of error bounds for the Stokes problem visualizes a relation of the LSFEM and the Ladyzhenskaya-Babuska-Brezzi (LBB) constant. This constant is a key in the existence and stability of solution to problems in fluid dynamics. The second part of this talk utilizes this relation to design a competitive numerical scheme for the computation of the LBB constant. The third part of the talk investigates the DPG method. This investigation relates the DPG method with the LSFEM. Hence, the results from the first part of this talk extend to the DPG method. This enables precise investigations of existing and the design of novel DPG schemes.

Numerical Analysis

Wed, 26.06.19 at 09:15

2.417

Neela Nataraj IIT Bombay

Morley FEM for a distributed optimal control problem governed by the von Karman equations

Abstract.

In this talk, we consider the distributed optimal control problem governed by the von Karman equations that describe the deflection of very thin plates defined on a polygonal domain of ℝ² with box constraints on the control variable. The talk discusses a numerical approximation of the problem that employs the Morley nonconforming finite element method to discretize the state and adjoint variables. The control is discretized using piecewise constants. A priori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions on the exact solution. Error estimates in lower order norms for the state and adjoint variables are derived. The lower order estimates for the adjoint variable and a post-processing of control leads to an improved error estimate for the control variable. Numerical results confirm the theoretical results obtained. This is a joint work with Sudipto Chowdhury and Devika Shylaja.

Numerical Analysis

Wed, 19.06.19 at 09:15

2.417

Gaddam Sharat IIT Bombay

A Posteriori Error Estimates of Discontinuous Galerkin Methods for the Elliptic Obstacle Problem

Abstract.

This is a continuation of the previous talk titled "Two New Approaches for Solving Elliptic Obstacle Problems Using Discontinuous Galerkin Methods". In this talk, we will construct the discrete Lagrange Multipliers for both the methods(Integral constraints method and Quadrature point constraints method) and also derive the optimal order(with respect to regularity) a priori error estimates. Later part of the talk focuses upon a posteriori error estimates where we will construct error estimators for both the methods and we will have a look at the reliability of the estimators. Finally, we conclude the talk by presenting the numerical experiments checking the reliability and efficiency of the estimators.

Numerical Analysis

Thu, 13.06.19 at 09:15

2.417

Mauro Perego

Generalized Moving Least Squares: Approximation Theory and Applications

Abstract.

(joint work with P. Bochev, P. Kuberry, N. Trask) In this talk we present existence and approximation results for the reconstruction of a few classes of linear functionals, including differential and integral functionals, using the Generalized Moving Least Square (GMLS) method. These results extend or specialize classical MLS theoretical results, and rely both on the classic approximation theory for finite elements and on existence/approximation results for scattered data. In particular, we will consider the reconstruction of vector fields in Sobolev spaces and the reconstruction of differential k-forms. We show how these results can be applied to data transfer problems and to design collocation and variational meshless schemes for the solution of partial differential equations.

Numerical Analysis

Wed, 12.06.19 at 09:15

2.417

Derk Frerichs HU Berlin

On pressure robustness and adaptivity of a Virtual Element Method for the Stokes problem

Abstract.

For the Stokes problem, many of the standard finite element method, e.g., Taylor-Hood, and also the virtual element method (VEM) proposed in [1] fail when it comes to small viscosity parameters ν or when the continuous pressure is complicated. In this talk, a modification of the VEM is presented which makes the method pressure robust, i.e., locking free for very small ν. For this purpose, a standard interpolation into Raviart-Thomas spaces of order k-1 will be employed which allows for a pressure robust modification of the discrete right hand side. In addition, an reliable error estimator is presented that makes adaptive mesh refinement possible. The presented numerical results will round up the presentation. [1] L. B. da Veiga, C. Lovadina, G. Vacca: Divergence free virtual elements for the Stokes problem on polygonal meshes. ESAIM: M2AN, 51(2). 2017

Numerical Analysis

Thu, 06.06.19 at 13:15

2.417

Gaddam Sharat IIT Bombay

Two New Approaches for Solving Elliptic Obstacle Problems Using Discontinuous Galerkin Methods

Abstract.

The main aim of the talk is to present two new ways to solve the elliptic obstacle problem by using discontinuous Galerkin finite element methods. In the talk, using the localized behaviour of DG methods, we discuss an optimal order(with respect to regularity) {\em a priori} error estimates, in 3 dimensions. We consider two different discrete sets, one with integral constraints and the other with nodal constraints at quadrature points. The analysis is carried out in a unified setting which holds true for several DG methods using quadratic polynomials.

Numerical Analysis

Thu, 06.06.19 at 09:15

2.417

Devika Shylaja IIT Bombay

The Hessian Discretisation Method for fourth order elliptic equations

Abstract.

Fourth order elliptic partial differential equations appear in various domains of mechanics. They model for example thin plates deformations as well as 2D turbulent flows through the vorticity formulation of Navier-Stokes equations. Many numerical methods, most of them are finite elements, have been developed over the years to approximate the solutions of these models. In this talk, we will present the Hessian Discretisation Method (HDM), a generic analysis framework that encompasses many numerical methods for fourth-order problems: conforming and nonconforming finite element methods, methods based on gradient recovery operators, and finite volume-based schemes. The principle of the HDM is to describe a numerical method using a set of four discrete objects, together called a Hessian Discretisation (HD): the space of unknowns, and three operators reconstructing respectively a function, a gradient and a Hessian. Each choice of HD corresponds to a specific numerical scheme. The beauty of the HDM framework is to identify four model-independent properties on an HD that ensure that the corresponding scheme converges for a variety of models, linear as well as non-linear.

Numerical Analysis

Wed, 05.06.19 at 09:15

3.007

Fleurianne Bertrand and Carsten Carstensen HU Berlin

A posteriori error estimation for HHO-methods - Part II

Numerical Analysis

Fri, 31.05.19 at 17:15

2.416

Michael Feischl TU Wien

Baysian FEM

Numerical Analysis

Wed, 29.05.19 at 09:15

3.007

Dietmar Gallistl University of Twente

Taylor-Hood discretization of the Reissner-Mindlin plate

Numerical Analysis

Wed, 22.05.19 at 09:15

3.007

Fleurianne Bertrand and Carsten Carstensen HU Berlin

A posteriori error estimation for HHO-methods

Numerical Analysis

Wed, 15.05.19 at 09:15

3.007

Friederike Hellwig HU Berlin

An adaptive lowest order dPG-FEM for linear elasticity

Numerical Analysis

Wed, 08.05.19 at 09:15

3.007

Philipp Bringmann HU Berlin

H&sup1 vector potentials for solenoidal vector fields with partial boundary conditions

Numerical Analysis

Wed, 24.04.19 at 09:15

3.007

Tien Tran-Ngoc HU Berlin

An adaptive lowest order dPG-FEM for the Stokes equations with optimal convergence rate

Numerical Analysis

Thu, 21.02.19 at 11:30

2.417

Tobias Tschirch Humboldt-Universität zu Berlin

Offsets of Non-Uniform Rational B-Spline curves for Computer Aided Design

Numerical Analysis

Wed, 13.02.19 at 10:00

Albert Cohen Paris

Optimal non-intrusive methods in high-dimension

Numerical Analysis

Wed, 06.02.19 at 09:15

2.417

Sophie Puttkammer Humboldt-Universität zu Berlin

Guaranteed Lower Eigenvalue Bounds with the Weak Galerkin FEM

Numerical Analysis

Wed, 30.01.19 at 09:15

2.417

Philipp Bringmann Humboldt-Universität zu Berlin

Quasi-optimal convergence of adaptive LSFEM for three model problems in 3D

Numerical Analysis

Wed, 16.01.19 at 09:15

2.417

Tien Tran-Ngoc Humboldt-Universität zu Berlin

Non-standard discretizations of a class of relaxed minimization problems

Numerical Analysis

Wed, 05.12.18 at 09:15

2.417

Rui Ma Humboldt-Universität zu Berlin

Adaptive mixed finite element methods for non-selfadjoint indefinite second-order elliptic PDEs with optimal rates

Abstract.

This talk establishes the convergence of adaptive mixed finite element methods for second-order linear non-selfadjoint indefinite elliptic problems in three dimensions with piecewise Lipschitz continuous coefficients. The error is measured in the L^2 norm of the flux variable and then allows for an adaptive algorithm with collective Dörfler marking. The axioms of adaptivity apply to this setting and guarantee the rate optimality for Raviart-Thomas and Brezzi-Douglas-Marini finite elements of any order for sufficiently small initial mesh-sizes and bulk parameter. Particular attention is laid out for the multiply connected polyhedral bounded Lipschitz domain and the quasi-interpolation of Nédélec finite elements.

Numerical Analysis

Wed, 28.11.18 at 09:15

2.417

Johannes Storn Humboldt-Universität zu Berlin

Advanced analysis of the DPG method

Abstract.

The functional analytical framework of the discontinuous Petrov-Galerkin (DPG) method bases on three hypotheses. Carstensen’s, Demkowicz’s, and Gopalakrishnan’s 2016 paper introduces a general guideline to verify the first two hypotheses. This talk modifies their approach. This modification improves existing results and allows for the design of well-posed DPG methods for parabolic and hyperbolic problems.

Numerical Analysis

Wed, 21.11.18 at 09:15

2.417

Derk Frerichs Humboldt-Universität zu Berlin

Introduction to the Virtual Element Method

Abstract.

This talk introduces the virtual element method that can be seen as an extension of finite element methods to polygonal and polyhedral meshes. The first part illustrates the core ideas and some implementation aspects in the discretisation of the Poisson model problem. The second part concerns an outlook to mixed problems, in particular the Stokes problem. The content of this talk is based on the papers "Basic principles of Virtual Element Methods", and "The Hitchhiker's Guide to the Virtual Element Method" by L. Beirao da Veiga, Franco Brezzi, Andrea Cangiani, Gianmarco Manzini, L. D. Marini, and Allessandro Russo.

Numerical Analysis

Wed, 14.11.18 at 09:15

3.007

Carsten Carstensen Humboldt-Universität zu Berlin

HLO methodology

Numerical Analysis

Wed, 07.11.18 at 09:15

2.417

Friederike Hellwig Humboldt-Universität zu Berlin

Adaptive Discontinuous Petrov-Galerkin Finite-Element-Methods

Numerical Analysis

Tue, 06.11.18 at 16:15

2.417

Thirupathi Gudi IISc Bangalore

Patch-wise local projection stabilized methods for convection-diffusion problem

Abstract.

In this talk, we discuss on two stabilized methods incorporating local projections on the patches of the basis functions of finite element spaces. The underlying finite element spaces can be either the conforming finite element space or the classical nonconforming finite element space. Numerical experiments illustrating the effect of the stabilization will be presented. This is joint work with Dr. Asha K. Dond.

Numerical Analysis

Fri, 02.11.18 at 14:15

2.417

Thirupathi Gudi IISc Bangalore

The obstacle problem

Numerical Analysis

Wed, 27.06.18 at 09:15

2.417 ...

Sophie Puttkammer Humboldt-Universität zu Berlin

A local a posteriori approximation error estimate for the companion operator

Numerical Analysis

Tue, 26.06.18 at 13:30

2.006

Lukas Gehring Humboldt-Universität zu Berlin

Adaptive Mesh Refinement via Newest Vertex Bisection in n Dimensions - Part III

Numerical Analysis

Wed, 20.06.18 at 13:30

2.006

Lukas Gehring Humboldt-Universität zu Berlin

Adaptive Mesh Refinement via Newest Vertex Bisection in n Dimensions - Part II

Numerical Analysis

Wed, 20.06.18 at 09:15

2.417

Georgi Mitsov Humboldt-Universität zu Berlin

Discontinuous Petrov-Galerkin Methods for the Time-Dependent Maxwell Equations

Numerical Analysis

Wed, 13.06.18 at 15:15

2.417

Dietmar Gallistl University of Twente

Numerical approximation of planar oblique derivative problems in nondivergence form

Numerical Analysis

Wed, 13.06.18 at 10:15

2.417

Tien Tran-Ngoc Humboldt-Universität zu Berlin

Non-standard Discretisation of a Class of Degenerate Convex Minimisation Problems

Numerical Analysis

Mon, 11.06.18 at 09:15

3.007

Lukas Gehring Humboldt-Universität zu Berlin

Adaptive Mesh Refinement via Newest Vertex Bisection in n Dimensions - Part VI

Numerical Analysis

Sun, 10.06.18 at 13:30

2.006

Lukas Gehring Humboldt-Universität zu Berlin

Adaptive Mesh Refinement via Newest Vertex Bisection in n Dimensions - Part V

Numerical Analysis

Wed, 06.06.18 at 09:15

2.417

Seungchan Ko University of Oxford

Finite element approximation of incompressible chemically reacting non-Newtonian fluids

Numerical Analysis

Wed, 30.05.18 at 09:15

2.417

Philipp Bringmann Humboldt-Universität zu Berlin

Quasi-optimal convergence of adaptive LSFEM in 3D

Numerical Analysis

Fri, 25.05.18 at 13:15

2.417

Stefan Sauter Universität Zürich

Estimating the effect of data simplification for elliptic PDEs

Numerical Analysis

Wed, 16.05.18 at 09:15

2.417

Rui Ma Humboldt-Universität zu Berlin

Guaranteed lower bounds for eigenvalues of elliptic operators in any dimension

Numerical Analysis

Wed, 09.05.18 at 09:15

2.417

Johannes Storn Humboldt-Universität zu Berlin

On the analysis of discontinuous Petrov-Galerkin methods

Numerical Analysis

Wed, 02.05.18 at 09:15

2.417

Friederike Hellwig Humboldt-Universität zu Berlin

Optimal convergence rates for adaptive lowest-order dPG methods

Numerical Analysis

Wed, 25.04.18 at 09:15

3.007

Daniel Peterseim Universität Augsburg

Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials

Numerical Analysis

Wed, 18.04.18 at 09:15

2.417

Gonzalo Gonzalez de Diego Universität Duisburg-Essen

Approximating the Cauchy stress tensor in hyperelasticity

Abstract.

In this presentation, a least squares finite element method (LSFEM) is presented for the first order system of hyperelasticity defined over the deformed configuration in order to approximate the Cauchy stress tensor. Unlike the first Piola-Kirchhoff stress tensor, the Cauchy stress tensor is symmetric, a property intimately related to the conservation of angular momentum. With this work, we wish to explore the possibility of imposing the symmetry of the stress tensor, strongly or weakly, in non-linear elasticity. Firstly, an overview of a LSFEM for hyperelasticity (over the reference configuration) by (Müller et al., 2014) is presented. Secondly, we address the question of under which conditions can a first order system over the deformed configuration be considered. Then, the former LSFEM is extended to the deformed configuration; we introduce a Gauss-Newton method for solving the non-linear minimization problem and show that, under small strains and stresses, the least-squares functional represents an a posteriori error estimator. Finally, we display numerical results for two test cases. These results indicate that this LSFEM is capable of giving reliable results even when the regularity assumptions from the analysis are not satisfied.

Research Seminar Numerical Analysis 📅