Analysis of a continuous Galerkin method with mesh modification for two-dimensional telegraph equation

Abstract

In this paper, we investigate the convergence of a space–time continuous Galerkin (STCG) method for two-dimensional (2-D) telegraph equation. The variable time steps and spatial mesh structures are allowed, which are necessary for adaptive computations on unstructured mesh. We demonstrate existence and uniqueness of the numerical solution and give a priori estimate in L∞(L2) norm without space–time mesh restrictions. The analysis method presented here develops and improves the existing theories so that it can be used to study the more general time-dependent partial differential equations (PDEs). Some numerical experiments are provided, and compared with the standard finite element (FE) method to confirm the high efficiency and the high accuracy for the proposed scheme.