A fast element-free Galerkin method for the fractional diffusion-wave equation

Abstract A fast element-free Galerkin (EFG) method is proposed for the numerical analysis of the fractional diffusion-wave equation. In this method, a fast time discrete scheme is first derived by applying the L1 and the fast H2N2 approximations to discretize the time Caputo fractional derivative, and then the Nitsche’s technique and the stabilized moving least squares approximation are adopted to establish linear algebraic systems. Based on the reproducing kernel gradient smoothing integration, an efficient numerical integration procedure is also presented to further accelerate the computations of the method. Theoretical error analysis of the fast EFG method is provided. Numerical results verify the efficiency of the method.