Seminar

des DFG-Sonderforschungsbereichs 393

Numerische Simulation auf massiv parallelen Rechnern

Zeit:	Freitag, 23.11.2001, 11:30 Uhr
Ort:	Reichenhainer Straße 41, Zi. 238
Vortragender:	Prof. Christoph Schwab (ETH Zürich)
Thema:	hp Discontinuous Galerkin Time-stepping for parabolic problems
We present an hp-Error analysis for the discontinuous Galerkin time-stepping scheme for abstract parabolic equations. We show for semidiscretization in time (Rothe's method) under realistic assumptions (polygonal or polyhedral domain, incompatible initial data, indefinite, nonselfadjoint spatial operators) that a) the method converges for large time-step size k as the temporal order r tends to infinity, and b) the error decreases exponentially with respect to the number of time degrees of freedom (i.e. the number of elliptic spatial problems to be solved). We describe a parallel implementation based on modal decoupling in time which reduces the CPU for one time step with any order r>=0 to that required by backward Euler. Numerical examples confirm the theory. This is joint work with D. Schoetzau (Minnesota/Basel). Referenzen: Time Discretization of parabolic problems by the $hp$-version of the discontinuous Galerkin finite element method (with D. Sch\"otzau), SIAM J. Numer. Analysis {\bf 38} (2000) 837-875. $hp$-Discontinuous Galerkin time-stepping for parabolic problems, Comp. Meth. Appl. Mech. Engg. {\bf 190} (2001) 6685-6708.
Das Seminar wird von Prof. Meyer geleitet. Interessenten sind herzlich eingeladen.