Research Seminar
WS 2015/16

Table of Conents


Organisation [ back ]

Prof. Dr. Carsten Carstensen
Contact: Friederike Hellwig (hellwigf@math.hu-berlin.de)

Location [ back ]

Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin
Room 2.417

Schedule [ back ]

Date Time Talk by Title
October 7, 2015 10:00 Neela Nataraj
(IIT Bombay) 		Finite Element Methods for Distributed Optimal Control Problems Governed by Plate Equations
October 14, 2015 09:15 Joscha Gedicke
(Universität Heidelberg) 		Numerical approximation of biharmonic eigenvalue problems
October 21, 2015 09:15 Sophie Puttkammer
(HU Berlin) 		Eine neue dPG Finite-Elemente-Methode niedriger Ordnung für Stokes Gleichungen
October 21, 2015 10:15 Johannes Storn
(HU Berlin) 		Die unstetige Petrov-Galerkin-Methode angewandt auf die zeitharmonischen Maxwell-Gleichungen
October 28, 2015 09:15 Tran Ngoc Tien
(HU Berlin) 		Least-Squares Finite-Elemente-Methode für die Stokes-Gleichungen in 3D
November 18, 2015 15:15 Mira Schedensack
(Universität Bonn) 		L2 best-approximation of the elastic stress in the Arnold-Winther FEM
November 19, 2015 10am-5pm V.A.
Variational Inequality Day (Workshop)
November 25, 2015 09:15 Pascal Huber
(Universität Bonn) 		Stability of the Rayleigh-Ritz method with piecewise polynomials of variable smoothness
November 26, 2015 14:15 Sören Bartels
(Universität Freiburg) 		Finite element approximation of functions of bounded variation
December 2, 2015 09:15 Franz Bethke
(HU Berlin) 		Least-Squares Methoden für lineare Elastizität
December 2, 2015 11:00 Daniel Peterseim
(Universität Bonn) 		Relaxing the CFL condition for the wave equation on non-uniform meshes
December 8, 2015 11:15 Fleurianne Bertrand
(Universität Duisburg-Essen) 		H(div) conforming elements on curved boundaries
December 16, 2015 09:15 Friederike Hellwig
(HU Berlin) 		The Primal dPG Method seen as a Least-Squares FEM
January 13, 2016 09:15 Johannes Storn
(HU Berlin) 		dPG for the ultra-weak variational formulation of Maxwell's equations
January 27, 2016 09:15 Felix Neumann
(HU Berlin) 		Über Fehlerabschätzungen bei einer druckrobusten und nichtkonformen Finite-Element-Methode für das Stokes-Problem unter minimaler Regularität
February 3, 2016 09:15 Kim Klüber
(HU Berlin) 		Modifikation einer dPG-Methode für lineare Elastizität
February 3, 2016 10:00 Tobias Steiner
(Leibniz Universität Hannover) 		Die dG-Methode in der linearen Elastizitätstheorie
February 10, 2016 09:15 Georgi Mitsov
(HU Berlin) 		Implicit Rothe's methods for the time-dependent Maxwell equations

Abstracts [ back ]

Speaker: Sören Bartels
Title: Finite element approximation of functions of bounded variation
Various phenomena involving free boundaries such as damage or plasticity require the description of physical quantities with discontinuous functions. One approach to their mathematical modeling is based on the space of functions of bounded variation which includes functions that are discontinuous and may jump across lower dimensional subsets. Numerical methods for their approximate solution are often based on regularizations which typically lead to restrictive conditions on discretization parameters. We try to avoid such modifications and discuss the convergence of discretizations with different finite element spaces, the iterative solution of the resulting finite-dimensional nonlinear systems of equations, and adaptive mesh-refinement techniques based on rigorous a posteriori error estimates for a model problem related to image processing. The application of the techniques to total variation flow, very singular diffusion processes, and segmentation problems will be addressed.

Archive [ back ]