Research Seminar
SS 2015

Table of Conents


Organisation [ back ]

Prof. Dr. Carsten Carstensen

Location [ back ]

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

Schedule [ back ]

Date Time Talk by Title
April 15, 2015 09:15 Mira Schedensack A class of mixed finite element methods based on the Helmholtz decomposition
April 22, 2015 09:15 Daniel Peterseim Eliminating the pollution effect in Helmholtz problems by local subscale correction
April 29, 2015 09:15 Johannes Storn Solving Maxwell's Equations using the dPG-Method - Theory
May 6, 2015 09:15 Franz Bethke Least-Squares Methoden für lineare Elastizität
May 13, 2015 09:15 Alessandro Masacci Nichtkonforme Finite-Elemente-Approximation eines Optimal-Design-Problems
May 20, 2015 09:15 Friederike Hellwig Remarks on the Data Approximation Error in a Low-Order dPG-FEM
May 27, 2015 09:15 Felix Neumann Fehlerabschätzungen einer druckrobusten-Modifikation des Crouzeix-Raviart Element
June 3, 2015 09:15 Loreen Gräber Free-discontinuity problem
June 8, 2015 09:15 Martin Brokate TBA
June 10, 2015 09:15 Daya Reddy Some issues concerning dissipative and energetic formulations of strain-gradient plasticity
June 17, 2015 09:15 Stefan Sauter Intrinsic Finite Element Methods
June 25, 2015 14:00 Daniele Boffi Adaptive finite element approximation of mixed eigenvalue problems
July 6, 2015 09:30 Andreas Schröder A-Posteriori-Fehlerkontrolle für h- und hp-Finite-Elemente-Methoden für Variationsungleichungen
July 8, 2015 09:15 Kim Klueber Modifikation einer dPG-Methode fuer lineare Elastizität
July 8, 2015 09:45 Friedrich W. Brockstedt Laufzeitverbesserungen für Refine3D mit C++

Abstracts [ back ]

Speaker: Daniel Peterseim
Title: Eliminating the pollution effect in Helmholtz problems by local subscale correction
A new Petrov-Galerkin multiscale method for the numerical approximation of high-frequency acoustic scattering problems will be presented. The discrete trial and test spaces are generated from standard mesh-based finite elements by local subscale corrections in the spirit of numerical homogenization. The precomputation of the corrections involves the solution of coercive cell problems on localized subdomains of size mH; H being the mesh size and m being the oversampling parameter. If the mesh size and the oversampling parameter are such that Hk and log(k)/m fall below some generic constants, the method is stable and its error is proportional to H; pollution effects are eliminated in this regime. For reference, see http://arxiv.org/pdf/1411.7512 and http://arxiv.org/abs/1503.04948.
Speaker: Daya Reddy
Title: Some issues concerning dissipative and energetic formulations of strain-gradient plasticity
Strain-gradient theories of plasticity have been extensively studied for some time, a key motivation being their relevance to modelling size effects at the mesoscale. Gradient terms may be incorporated into the models in energetic or dissipative form, or through a combination of both. Energetic formulations are based on the inclusion in the free energy of a plastic energy that depends on some measure of the strain gradients. On the other hand dissipative formulations extend the classical associative flow relations to give a generalized plastic strain rate in terms of a generalized stress. These two approaches lead to variational formulations which have quite distinctive features, and which lead to distinct challenges in the development of solution algorithms and numerical analyses. The aims of this presentation are to present an overview of a rate-independent model of strain-gradient plasticity, to illustrate the theoretical and numerical features of energetic and dissipative formulations, and to discuss the implications for modelling plastic behaviour at the mesoscale.
Speaker: Stefan Sauter
Title: Intrinsic Finite Element Methods
In this talk we consider an intrinsic approach for the direct computation of the fluxes for problems in potential theory. We present a general method for the derivation of intrinsic conforming and non-conforming finite element spaces and appropriate lifting operators for the evaluation of the right-hand side from abstract theoretical principles related to the second Strang Lemma. This intrinsic finite element method is analyzed and convergence with optimal order is proved.
Speaker: Daniele Boffi
Title: Adaptive finite element approximation of mixed eigenvalue problems
We show that the h-adaptive mixed finite element method for the discretization of the eigenvalues of Laplace operator produces optimal convergence rates in terms of nonlinear approximation classes. The results are valid for the typical mixed spaces of Raviart-Thomas or Brezzi-Douglas-Marini type with arbitrary fixed polynomial degree in two and three dimensions. Our theory is cluster robust, in the sense that it allows for the simultaneous optimal approximation of the eigenvalues belonging to the same cluster. This is a joint work with D. Gallistl, F. Gardini, and L. Gastaldi.

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