Otto-von-Guericke-Universität Magdeburg


Prof. Dr. Arnold Reusken

Space-time trace FEM for PDEs on evolving surfaces

We present a particular class of finite element methods for the solution of partial differential equations on evolving surfaces. The evolving hypersurface in Rd defines a d-dimensional space-time manifold in the space-time continuum in Rd+1. We derive and analyze a variational formulation for a class of diffusion problems on the space-time manifold. For this variational formulation new well-posedness and stability results are derived. The analysis is based on an inf-sup condition and involves some natural, but non-standard, (anisotropic) function spaces. Based on this formulation a discrete in time variational formulation is introduced that is very suitable as a starting point for a discontinuous Galerkin (DG) space-time finite element discretization. This FEM employs discontinuous piecewise linear in time – continuous piecewise linear in space finite elements. Trial and test surface finite element spaces consist of traces of standard volumetric elements on the space-time manifold. This DG space-time method is explained and results of numerical experiments are presented that illustrate its properties. Results of a discretization error analysis are briefly addressed.

Datum: 12.05.2016, Raum: G03-106, Zeit: 17:00
Letzte Änderung: 16.11.2016 - Ansprechpartner: Prof. Dr. Volker Kaibel
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