An energy-based discontinuous Galerkin method with tame CFL numbers for the wave equation

We extend and analyze the energy-based discontinuous Galerkin method for second order wave equations on staggered structured meshes. By combining spatial staggering with local time-stepping near boundaries, overcomes typical numerical stiffness associated high piecewise polynomial approximations. In one space dimension periodic boundary conditions suitably chosen fluxes, we prove bounds operators that establish stability CFL numbers \(c \frac{\Delta t}{h} < C\) independent of when stability-enhanced explicit schemes matching are used. For problems bounded domains in higher dimensions demonstrate numerically can march explicitly large time steps at temporal accuracy.