Research Seminar
SoSe 2023

Table of Contents


Organization [ back ]

Prof. Carsten Carstensen
Contact: Benedikt Gräßle (graesslb(at)math.hu-berlin.de)

The seminar talks usually take place on Tuesday at 1 pm.

The announcements for each talk will be sent via a mailing list. Please contact Benedikt Gräßle (graesslb(at)math.hu-berlin.de) if you want to join the list.

Location [ back ]

Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin
House 2, Floor 4, Room 2.417

Schedule [ back ]

Date Time Talk by Title Room
April 19, 2023 13:15 Benedikt Gräßle (HU Berlin) The hierarchical Argyris AFEM with optimal convergence rates 2.417
April 25, 2023 13:15 Georgi Mitsov (HU Berlin) Combining time-stepping θ-schemes with dPG-FEM for the solution of the heat equation 2.417
May 02, 2023 13:15 Stefan Sauter (Uni Zürich) The method of integral equations for acoustic transmission problems with varying coefficients 2.417
May 09, 2023 13:15 Lara Théallier (HU Berlin) Implementing HHO for linear elasticity 2.417
May 10, 2023 14:45 Neela Nataraj (IIT Bombay) Discussion on WOPSIP 2.417
May 16, 2023 13:15 Felix Goldmann (HU Berlin) Discontinuous Galerkin method for the Parabolic Obstacle Problem 2.417
May 16, 2023 15:00 Ngoc Tien Tran (Uni Jena) Minimal residual methods for PDE of second order in nondivergence form 2.417
May 23, 2023 13:15 Johannes Storn (Uni Bielefeld) Advantages of Dual Formulations in Computational Calculus of Variations 2.417
May 30, 2023 13:15 Joscha Gedicke (Uni Bonn) P₁ finite element methods for an elliptic optimal control problem with pointwise state constraints 2.417
June 06, 2023 13:15 Carsten Carstensen (HU Berlin) Smoother 2.006
June 13, 2023 13:15 Emilie Pirch (Uni Jena) Guaranteed lower eigenvalue bounds with three skeletal methods 2.417
June 20, 2023 13:15 Benedikt Gräßle (HU Berlin) The pressure-wired Stokes element 2.417
July 06, 2023 15:15 Mira Schedensack (Uni Leipzig) Discrete Helmholtz decompositions Uni Leipzig
July 06, 2023 16:45 Carsten Carstensen (HU Berlin) Lower eigenvalue bounds of the Laplacian Uni Leipzig
July 07, 2023 09:15 Lara Théallier (HU Berlin) HHO for linear elasticity Uni Leipzig
July 07, 2023 10:45 Jonas Ketteler (Uni Leipzig) Some ideas for the quasi-orthogonality for the Fortin-Soulie FEM Uni Leipzig
July 07, 2023 12:15 Benedikt Gräßle (HU Berlin) Stabilization-free a posteriori error analysis for hybrid-high order methods Uni Leipzig
July 11, 2023 13:15 Norbert Heuer (PUC Chile) Conforming Galerkin schemes via traces and applications to plate bending -- Teil 1 2.417
July 11, 2023 15:15 Norbert Heuer (PUC Chile) Conforming Galerkin schemes via traces and applications to plate bending -- Teil 2 2.417

Abstracts [ back ]

Speaker: Stefan Sauter
Title: The method of integral equations for acoustic transmission problems with varying coefficients
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.
Speaker: Johannes Storn
Title: Advantages of Dual Formulations in Computational Calculus of Variations
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.
Speaker: Joscha Gedicke
Title: P₁ finite element methods for an elliptic optimal control problem with pointwise state constraints
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.
Speaker: Benedikt Gräßle
Title: The pressure-wired Stokes element
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.

Archive [ back ]