Unconditional stability and optimal error estimates of discontinuous Galerkin methods for the second-order wave equation

Abstract

In this paper, we revisit the numerical solution of the scalar second-order wave equation by discontinuous Galerkin methods. The numerical methods are different from the ones found in existing literature. Moreover, we provide a stability analysis and derive optimal order error estimates through a more direct approach. The error estimate in an -like norm is derived based on an analysis of the truncation error while that in the norm based on an application of the Aubin-Nitsche technique. Numerical simulation results are reported in support of the theoretical error estimates.