Discontinuous Galerkin discretization in time of systems of second-order nonlinear hyperbolic equations

In this paper we study the finite element approximation of systems of second-order nonlinear hyperbolic equations. The proposed numerical method combines a hp -version discontinuous Galerkin finite element approximation in the time direction with an H 1 (Ω)-conforming finite element approximation in the spatial variables. Error bounds at the temporal nodal points are derived under a weak restriction on the temporal step size in terms of the spatial mesh size. Numerical experiments are presented to verify the theoretical results.