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.
© de Gruyter 2010