P0 time/space subcell limiting DG-DGLM method for hyperbolic systems of conservation laws

Abstract A high order discontinuous Galerkin method with Lagrange multiplier (DGLM) in space combined with discontinuous Galerkin (DG) method in time (DG-DGLM) [32] is numerically investigated for the approximation of the solution to the system of hyperbolic conservation laws. Computation is done in element by element fashion. P 0 time and space subcell limiting processes are applied to resolve the shocks. It is numerically shown that the high order DG-DGLM method is well-suited for long time integrations. Several numerical experiments for advection, shallow water, and compressible Euler equations are presented to show the performance of the high order DG-DGLM with P 0 time and space subcell limiting processes.