Efficient time integration for discontinuous Galerkin approximations of linear wave equations

摘要

We consider the combination of discontinuous Galerkin discretizations in space with various time integration methods for linear acoustic, elastic, and electro-magnetic wave equations. For the discontinuous Galerkin method we derive explicit formulas for the full upwind flux for heterogeneous materials by solving the Riemann problems for the corresponding first-order systems. In a framework of bounded semigroups we prove convergence of the spatial discretization.