Research Seminar
WS 2017/18

Table of Contents


Organisation [ back ]

Prof. 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 19, 2017 09:15 Johannes Storn
(HU Berlin) 		Asymptotic Exactness of the dPG Method
October 26, 2017 09:15 Nando Farchmin
(HU Berlin) 		A Discontinuous Petrov-Galerkin Finite Element Method for a Model Problem in Topology Optimization
November 2, 2017 09:15 Carsten Carstensen
(HU Berlin) 		Optimal Convergence Rates for Adaptive Lowest Order Discontinuous Petrov-Galerkin Method
November 2, 2017 14:00 Carsten Carstensen
(HU Berlin) 		Optimal Convergence Rates for a Least-Squares Method
November 9, 2017 09:15 Stephan Schwöbel
(HU Berlin) 		Über den Zusammenhang zwischen 4 dPG-FEM und gewichteten LS-FEM
November 16, 2017 14:30 Tomáš Vejchodský
(The Czech Academy of Sciences, Prague) 		Flux reconstructions and lower bounds on eigenvalues
November 16, 2017 15:00 Joscha Gedicke
(Universität Wien) 		Adaptive Arnold-Winter finite element methods for Stokes eigenvalue problems
November 23, 2017 09:15 Zaven Badalyan
(HU Berlin)		 Eine primale dPG Methode für nichtlineare Elastizität
November 30, 2017 09:15 Tran Ngoc Tien
(HU Berlin) 		CR = dRT in convex minimisation problem
December 7, 2017 09:15 Lukas Gehring
(HU Berlin) 		Adaptive Verfeinerung in n Dimensionen, binäre Wälder (Teil I)
December 14, 2017 09:15 Lukas Gehring
(HU Berlin) 		Adaptive Verfeinerung in n Dimensionen, binäre Wälder (Teil II)
December 21, 2017 09:15 Lukas Gehring
(HU Berlin) 		Adaptive Verfeinerung in n Dimensionen, binäre Wälder (Teil III)
January 11, 2018 09:15 Johannes Storn
(HU Berlin) 		Guaranteed upper eigenvalue bounds with LSFEM
January 18, 2018 09:15 Philipp Bringmann
(HU Berlin) 		On the approximation of Dirichlet boundary conditions in R³
January 22, 2018 11:00 Fleurianne Bertrand
(Universität Duisburg-Essen)
January 24, 2018 09:15 Dietmar Gallistl
(Karlsruher Institut für Technologie) 		A robust discretization of the Reissner-Mindlin plate with arbitrary polynomial degree
February 1, 2018 09:15 Sophie Puttkammer
(HU Berlin)
February 6, 2018 15:15 Studierende des Projektpraktikums II
February 15, 2018 09:15 Stephan Daniel Schwöbel
(HU Berlin) 		Über den Zusammenhang von 4 dPG-FEM mit gewichteten LS-FEM

Abstracts [ back ]

Speaker: Tomáš Vejchodský
Title: Flux reconstructions and lower bounds on eigenvalues
Computing lower bounds on eigenvalues of symmetric elliptic second-order partial differential operators is a challenging problem. It has been studied for many decades and among the variety of approaches the Lehmann-Goerisch method is one of the most successful. The Lehmann-Goerisch method is based on conforming approximations of eigenfunctions, certain a priori known (and perhaps rough) lower bound on some eigenvalue and a flux reconstruction, which is traditionally computed by solving a large saddle point problem by mixed finite element problem. The talk will review the Lehmann-Goerisch method and show that rather than solving the large mixed finite element problem, we can straightforwardly utilize modern flux reconstruction techniques known from the source problems. This flux reconstruction can be computed locally and in parallel by solving a sequence of small independent problems. It enables to use finer meshes and achieve higher accuracy than the traditional approach.
Speaker: Joscha Gedicke
Title: Adaptive Arnold-Winter finite element methods for Stokes eigenvalue problems
Over the last decade, the a posteriori error analysis of eigenvalue problems using finite element approximations has been well developed. However, most results are for the Laplace eigenvalue problem and only a few papers consider the a posteriori error analysis for the Stokes eigenvalue problem. In this talk we present the a priori and a posteriori error analysis for the Stokes eigenvalue problem based on higher order finite elements which enables high order approximations of Stokes eigenvalues. We study the Arnold-Winter mixed finite element formulation for the two-dimensional Stokes eigenvalue problem using the stress-velocity formulation. We present a priori error estimates for eigenvalues and eigenfunctions. To improve the approximation of the eigenvalues, we derive a local postprocessing. For smooth data we prove higher order convergence of the postprocessed eigenvalues. With the help of the higher order local postprocessing, we develop a reliable a posteriori error estimator for the eigenvalue error. We discuss several numerical examples to validate the theoretical higher order convergence of the postprocessing and the reliability and empirical efficiency of the derived a posteriori error estimator. This is joint work with Arbaz Khan.
Speaker: Dietmar Gallistl
Title: A robust discretization of the Reissner-Mindlin plate with arbitrary polynomial degree (joint work with M. Schedensack)
The transverse displacement w of a thin elastic plate of thickness t>0 and the rotation φ of the plate's fibers normal to the mid-surface can be described by the Reissner--Mindlin plate model. Standard schemes are known to exhibit shear locking and yield poor results for small thickness t << h. It was the observation of Brezzi and Fortin (1986) that the Helmholtz decomposition of the shear variable ζ := t-2 (∇ w - φ) may serve as the key for the robust numerical approximation of this problem. Arnold and Falk (1989) discovered a discrete analogue to that decomposition which led to a robust nonconforming finite element discretization. Their discrete Helmholtz decomposition turned out useful for other purposes, too; but in its original form it is restricted to piecewise affine finite element functions and so to the lowest-order case. This talk proposes a new numerical scheme for the Reissner--Mindlin plate model. The method is based on a discrete Helmholtz decomposition and can be viewed as a generalization of the nonconforming finite element scheme of Arnold and Falk. The two unknowns in the discrete formulation are the in-plane rotations and the gradient of the vertical displacement. In the stability and error analysis, the decomposition of the discrete shear variable leads to equivalence with the usual Stokes system with penalty term plus two Poisson equations and the proposed method is equivalent to a stabilized discretization of the Stokes system that generalizes the Mini element. The method is proved to satisfy a best-approximation result which is robust with respect to the thickness parameter t.

Archive [ back ]