Research Seminar
SS 2020

Table of Contents


Organization [ back ]

Prof. Carsten Carstensen
Contact: Sophie Puttkammer (puttkams(at)math.hu-berlin.de)

Location [ back ]

Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin
Room 2.417 or Room 3.007

Until further notice the seminar will take place online. There exists an associated Moodle course FS Numerische Mathematik (SoSe2020), which contains the links for the zoom meeting. The passwort for the Moodle course or the information concerning the Zoom meeting can be send per Email on request.



Schedule [ back ]

Date Time Talk by Title Room
April 20, 2020 11:15 Fleurienne Bertrand
(HU Berlin) 		First order least-squares formulations for eigenvalue problems online
April 29, 2020 9:15 Rui Ma
(Universität Duisburg Essen) 		Adaptive least-squares finite element methods for non-selfadjoint indefinite second-order linear elliptic problems online
May 6, 2020 17:00 Carsten Carstensen
(HU Berlin) 		Abstract nonconforming schemes online
May 13, 2020 17:15 Sophie Puttkammer
(HU Berlin) 		Notes on Morley in 3D online
May 20, 2020 17:15 Jörn Wichmann
(Universität Bielefeld) 		The parabolic p-Laplacian with fractional differentiability online
May 27, 2020 17:15 Johannes Storn
(Universität Bielefeld) 		On the Sobolev and Lp stability of the L² projection online
June 3, 2020 17:15 Philipp Bringmann
(HU Berlin)		 Towards an efficient implementation of newest-vertex bisection with separate marking in MATLAB online
June 10, 2020 17:15 Tien Tran-Ngoc
(HU Berlin) 		Unstabilized Hybrid High-Order method for a class of degenerate convex minimization problems online
June 10, 2020 18:00 Carsten Carstensen
(HU Berlin) 		Introduction to dG4plates online
June 17, 2020 17:15 Henrik Schneider
(HU Berlin) 		DPG for Laplace eigenvalue problem online
June 24, 2020 17:15 Julian Streitberger
(HU Berlin)		 C0 interior penalty methods for the biharmonic problem online
July 1, 2020 17:15 Emilie Pirch
(HU Berlin) 		Introduction and implementation of an HHO method online
July 8, 2020 17:15 Georgi Mitsov
(HU Berlin) 		Elements of stability analysis for the heat equation online
July 15, 2020 17:15 Tien Tran-Ngoc
(HU Berlin) 		GPU computing in MATLAB for a higher-order method online

Abstracts [ back ]

Speaker: Fleurienne Bertrand
Title: First order least-squares formulations for eigenvalue problems
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.
Speaker: Ma Rui
Title: Adaptive least-squares finite element methods for non-selfadjoint indefinite second-order linear elliptic problems
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.
Speaker: Jörn Wichmann
Title: The parabolic p-Laplacian with fractional differentiability
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.
Speaker: Johannes Storn
Title: On the Sobolev and Lp stability of the L² projection
This talk investigates the stability of the L² projection onto Lagrange finite element spaces with respect to Lp and Sobolev norms. It motivates the investigation by emphasising the importance of the stability in the numerical analysis of the parabolic problems. Thereafter, the talk introduces a locally defined operator that approximates the L² projector. This operator allows to estimate the decay of the L² projection and so leads to stability estimates with respect to weighted L² norms. We extend these estimates to Lp and Sobolev norms.

The talk bases on joint work with Lars Diening and Tabea Tscherpel.
Speaker: Tien Tran-Ngoc
Title: Unstabilized Hybrid High-Order method for a class of degenerate convex minimization problems
The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided p-growth. The minimizers may be non-unique in the primal variable but the unique stress σ enjoys some higher smoothness σ∈ W1,p'loc(Ω;M). Examples include the p-Laplacian, an optimal design problem in topology optimization, and the convexified double-well problem. The approximation by hybrid high-order methods (HHO) utilizes a reconstruction of the gradients with piecewise Raviart-Thomas or BDM finite elements without stabilization on a regular triangulation into simplices. The application of this HHO method to the class of degenerate convex minimization problems allows for a unique H(div) conforming stress approximation σh. The main results are a priori and a posteriori error estimates for the stress error σ - σh in Lebesgue norms and a computable lower energy bound. Numerical benchmarks display higher convergence rates for higher polynomial degrees and include adaptive mesh-refining with the first superlinear convergence rates of guaranteed lower energy bounds.

Archive [ back ]