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2009-24

A stable discontinuous Galerkin-Petrov time discretization of higher order

by Schieweck, F..


Series: 2009-24, Preprints

MSC:
65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65M12 Stability and convergence of numerical methods
65M15 Error bounds

Abstract:
We construct and analyze a discontinuous Galerkin-Petrov time
discretization of a general evolution equation in a Hilbert space.
The method is A-stable and exhibits an energy decreasing property.
The approach consists in a continuous solution space and a
discontinuous test space such that the time derivative of the
discrete solution is contained in the test space. This is the key
to get stability.
We prove A-stability and optimal error estimates.
Numerical results confirm the theoretical results.

Keywords:
discontinuous finite elements, Galerkin-Petrov method, stability and error estimates