Graduate Seminar "Aktuelle Themen der Numerik"

Thursday, Nov 14, 2013, 02:00 pm

An Eulerian space-time finite element method for diffusion problems on evolving surfaces

Prof. Arnold Reusken (IGPM, RWTH Aachen)

We introduce a new class of finite element discretization 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 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 presented. 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 DG method is nonstandard in the sense that the trace on the space-time manifold of a Eulerian outer finite
element space in Rd+1 is used as a finite element space on the evolving hypersurface. The DG space-time method is explained and discretization error bounds are discussed. Results of numerical experiments are presented that illustrate properties of this finite element method.

Time: 02:00 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen