Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37966 ; Department of Applied Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece; IACM-FORTH, 711 10 Heraklion, Crete, Greece
Abstract:
We consider space-time continuous Galerkin methods with mesh modification in time for semilinear second order hyperbolic equations. We show a priori estimates in the energy norm without mesh conditions. Under reasonable assumptions on the choice of the spatial mesh in each time step we show optimal order convergence rates. Estimates of the jump in the Riesz projection in two successive time steps are also derived.