Error estimates of a semi-discrete LDG method for the system of damped acoustic wave equation

Abstract

Abstract We consider a system of acoustic wave equation possessing lower-order perturbation terms in a bounded domain in R2 $\mathbb{R}^{2}$. In this paper, we show the system is well-posed and stable with energy decays introducing a local discontinuous Galerkin (LDG) method. Also, we study an a priori L2 $L^{2}$-norm error estimate for the semi-discretized LDG method for the system under additional regularity assumptions. Further, numerical tests are presented to support the theoretical analysis.

Keywords

• Local discontinuous Galerkin method
• Damped acoustic wave equation
• A-priori error estimates