University of Twente
Electrical Engineering, Mathematics and Computer Science
Campus building Zilverling 3004
7522 NB Enschede
P.O. Box 217
7500 AE Enschede
University of Twente
Mathematics of Computational Science
Special focus on: Inverse Problems, Discontinuous Galerkin Methods, Nonlinear PDE's, Adaptivity
(Co-organisation with Matthias Schlottbom and Gerhard Starke)
The aim of this small-scale, week-long interactive mini-workshop jointly organized by the University of Duisburg-Essen and the University of Twente, and kindly hosted at the MFO, is to bring together experts in non-standard and mixed finite elements methods with experts in the field of electromagnetism.
Abstract: Finite element methodologies dominate the computational approaches for the solution to partial differential equations and nonstandard finite element schemes most urgently require mathematical insight in their design. The hybrid workshop vividly enlightened and discussed innovative nonconforming and polyhedral methods, discrete complex-based finite element methods for tensor-problems, fast solvers and adaptivity, as well as applications to challenging ill-posed and nonlinear problems.
This workshop was about the numerical solution of PDEs for which classical
such as the finite element method, are not well suited or need further
I was invited to talk about the new results on Least-Squares methods for the approximation of Eigenvalues
We are organizing this workshop Least-Squares Finite Element Methods and Discontinuous Petrov Galerkin Methods at HU Berlin from September 16th to September 18th, 2019.
The decision of the German Research Foundation to support the MATH+ Cluster of Excellence gave reason to the Grand Opening. On 14 May 2019, 800 invited guests met in the Berlin Kosmos and spent entertaining moments together and celebrating the great success that is an outstanding achievement for the city of Berlin and for science in Berlin. Among the guests were many renowned scientists and numerous politicians such as State Secretary Steffen Krach.
Minisymposium on Adaptive and property preserving finite element methods, jointly organised with Pavel Bochev (Sandia National Laboratories, USA) and Jörg Schröder (UDE, Germany)
I presented the new a posteriori error estimates for the three-field variational formulation of the Biot problem involving the displacements, the total pressure and the fluid pressure of this paper with my Co-author Gerhard Starke.
The discretization under focus is the conforming Taylor–Hood finite element combination, consisting of polynomial degrees for the displacements and the fluid pressure and for the total pressure. The symmetry of the reconstructed stress is allowed to be satisfied only weakly. The reconstructions can be performed locally on a set of vertex patches and lead to a guaranteed upper bound for the error with a constant that depends only on local constants associated with the patches and thus on the shape regularity of the triangulation. Particular emphasis is given to nearly incompressible materials and the error estimates hold uniformly in the incompressible limit. Numerical results on the L-shaped domain confirm the theory and the suitable use of the error estimator in adaptive strategies.
We are so glad to welcome as speaker
S. Sauter (Universität Zürich)
J. Gedicke (Universität Wien)
D. Peterseim (Universität Augsburg)
T. Vejchodsky (Czech Academy of Sciences)
M. Vohralik (Inria research centre Paris)
J. Storn (Humboldt-Universität zu Berlin)
R. Ma (Humboldt-Universität zu Berlin)
D. Boffi (Università di Pavia)
F. Bertrand (Humboldt-Universität zu Berlin)
With my Co-author Prof. Daniele Boffi we presented our work on a posteriori error estimates for the mixed numerical approximation of the Laplace eigenvalue problem using a reconstruction in the standard conforming space for the primal variable of the mixed Laplace eigenvalue problem. This work compare it with analogous approaches present in the literature for the corresponding source problem. In the case of Raviart–Thomas finite elements of arbitrary polynomial degree, the resulting error estimator constitutes a guaranteed upper bound for the error and is shown to be local efficient. Our reconstruction is performed locally on a set of vertex patches.
I received the Post-Doc Award of the mathematical faculty of Essen for my work on parametric finite elements for the mixed approximation of PDEs on domains with curved boundaries.
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