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. P0 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 P0 time and space subcell limiting processes.
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