Fully discrete local discontinuous Galerkin method for solving the fractional telegraph equation

Abstract

This paper aims to develop a fully discrete local discontinuous Galerkin finite element method for numerical simulation of the time-fractional telegraph equation, where the fractional derivative is in the sense of Caputo. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. The stability and convergence of this discontinuous approach are discussed and theoretically proven. Finally numerical examples are performed to illustrate the effectiveness and the accuracy of the method.