A continuous Galerkin method for pseudo-hyperbolic equations with variable coefficients

Abstract

This paper, we study a space-time continuous Galerkin (STCG) method with mesh change for two-dimensional (2-D) pseudo-hyperbolic equations with variable coefficients, which gives the same treatment for time and space discretizations, namely both time and space variables are discretized via finite element (FE) method. In addition, it allows the change of time step and space mesh which are necessary for adaptive algorithms. We prove the existence and uniqueness of approximation solution and give a prior error estimate without any conditions attached to the space-time grid. Finally, a numerical example is given to confirm the feasibility to the scheme constructed here.