by Schieweck, F..
Series: 2009-24, Preprints
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.
discontinuous finite elements, Galerkin-Petrov method, stability and error estimates