Numerical solution of the viscoelastic wave equation by Galerkin spectral element method

In this paper, the Galerkin spectral element method (GSEM) is presented for solving the one-dimensional viscoelastic wave equation. The finite difference approximation is applied for temporal discretization, and the convergence order of the technique is demonstrated. An a priori error estimate is determined for the total-discrete system. The computational efficiency of the method is confirmed through a numerical example, which shows that the method is effectively applicable.