Discontinuous Galerkin method for the diffusive-viscous wave equation

This paper develops and analyzes the discontinuous Galerkin method for the diffusive-viscous wave equation. The proposed numerical scheme is established by using the discontinuous Galerkin discretization for the spatial variable and a tailored finite difference scheme to approximate the first and second order temporal derivative terms. A second order temporal convergence rate and the optimal order spatial error estimate in the DG norm are derived. We also provide the optimal spatial error estimate in the L-2(omega)-norm under the extra parameter assumption. Numerical tests are presented to illustrate the predicted convergence behaviours and the versatility of the proposed method. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.