Research Seminar
WS 2018/19

Table of Contents


Organisation [ back ]

Prof. Carsten Carstensen
Contact: Johannes Storn (storn@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



Schedule [ back ]

Date Time Talk by Title Room
November 2, 2018 14:15 Thirupathi Gudi
(IISc Bangalore) 		The obstacle problem 2.417
November 6, 2018 16:15 Thirupathi Gudi
(IISc Bangalore) 		Patch-wise local projection stabilized methods for convection-diffusion problem 2.417
November 7, 2018 09:15 Friederike Hellwig
(Humboldt-Universität zu Berlin) 		Adaptive Discontinuous Petrov-Galerkin Finite-Element-Methods 2.417
November 14, 2018 09:15 Carsten Carstensen
(Humboldt-Universität zu Berlin) 		HLO methodology 3.007
November 21, 2018 09:15 Derk Frerichs
(Humboldt-Universität zu Berlin) 		Introduction to the Virtual Element Method 2.417
November 28, 2018 09:15 Johannes Storn
(Humboldt-Universität zu Berlin)		 Advanced analysis of the DPG method 2.417
December 5, 2018 09:15 Rui Ma
(Humboldt-Universität zu Berlin)		 Adaptive mixed finite element methods for non-selfadjoint indefinite second-order elliptic PDEs with optimal rates 2.417
January 16, 2019 09:15 Tien Tran-Ngoc
(Humboldt-Universität zu Berlin) 		Non-standard discretizations of a class of relaxed minimization problems 2.417
January 18-19, 2019 All day Various speakers 18th-GAMM-Seminar on Microstructures
January 30, 2019 09:15 Philipp Bringmann
(Humboldt-Universität zu Berlin) 		Quasi-optimal convergence of adaptive LSFEM for three model problems in 3D 2.417
February 6, 2019 9:15 Sophie Puttkammer
(Humboldt-Universität zu Berlin) 		Guaranteed Lower Eigenvalue Bounds with the Weak Galerkin FEM 2.417
February 13, 2019 10:00 Albert Cohen
(Paris) 		Optimal non-intrusive methods in high-dimension
February 21, 2019 11:30 Tobias Tschirch
(Humboldt-Universität zu Berlin) 		Offsets of Non-Uniform Rational B-Spline curves for Computer Aided Design 2.417

Abstracts [ back ]

Speaker: Thirupathi Gudi
Title: Patch-wise local projection stabilized methods for convection-diffusion problem
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.
Speaker: Derk Frerichs
Title: Introduction to the Virtual Element Method
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.
Speaker: Johannes Storn
Title: Advanced analysis of the DPG method
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.
Speaker: Rui Ma
Title: Adaptive mixed finite element methods for non-selfadjoint indefinite second-order elliptic PDEs with optimal rates
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.

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