Error analysis of direct discontinuous Galerkin method for two-dimensional fractional diffusion-wave equation

Abstract Based on the finite difference scheme in temporal and the direct discontinuous Galerkin (DDG) method in spatial, a fully discrete DDG scheme is first proposed to solve the two-dimensional fractional diffusion-wave equation with Caputo derivative of order 1  α O ( Δ t + h k + 1 ) is derived in L 2 norm with P k polynomial. Numerical experiments are presented to demonstrate the theoretical results.