09-24
A stable discontinuous Galerkin-Petrov time discretization of higher order
Preprint series: 09-24, 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
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