A mixed discontinuous Galerkin method for the wave equation. (15th January 2021) - He, Limin; Wang, Fei; Wen, Jing
Abstract: We study a mixed discontinuous Galerkin (DG) method for solving the second-order wave equation. The stress variable p and the displacement variable u are discretized by the mixed DG element pair P k + 1 – P k ( k ≥ 0 ). Under appropriate regularity assumptions on the solution pair, we derive optimal error estimates for the spatially semi-discrete scheme. Specifically, we prove the optimal convergence orders for u in L 2 norm and p in L 2 norm. Some test problems are presented, and the numerical results show that the orders of convergence coincide with the predicted error estimates.