A Space-Time Interior Penalty Discontinuous Galerkin Method for the Wave Equation

Abstract A new higher-order accurate space-time discontinuous Galerkin (DG) method using the interior penalty flux and basis functions, both in space time, is presented fully analyzed for second-order scalar wave equation. Special attention given to definition of numerical fluxes since they are crucial stability accuracy DG method. The theoretical analysis shows that discretization stable converges a DG-norm on general unstructured locally refined meshes, including local refinement time. does not have CFL-type restriction stability. Optimal order obtained if mesh size h time step $$\Delta t$$ ? t satisfy $$h\cong C\Delta h ? C , with C positive constant. optimal confirmed by calculations several model problems. These also show p th-order tensor product functions convergence rate $$L^\infty$$ L ? $$L^2$$ 2 -norms $$p+1$$ p + 1 polynomial orders $$p=1$$ = $$p=3$$ 3 $$p=2$$ .