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

摘要

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 < 2. The proposed scheme is unconditional stable, and the spatial global convergence and the temporal convergence order of O(Δt+hk+1) is derived in L2 norm with Pk polynomial. Numerical experiments are presented to demonstrate the theoretical results.