High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes

摘要

Employing finite element method in spatial direction and Crank-Nicolson scheme in temporal direction, a fully discrete scheme with high accuracy is established for a class of two-dimensional time fractional diffusion-wave equation with Caputo fractional derivative. Unconditional stability analysis of the approximate scheme is proposed. The spatial global superconvergence and temporal convergence of order O(h(2) + tau(3-alpha)) for the original variable in H-1-norm is presented by means of properties of bilinear element and interpolation postprocessing technique without Ritz projection, where h and tau are the step sizes in space and time, respectively. Finally, several numerical results are implemented to evaluate the efficiency of the theoretical results on both regular and anisotropic meshes.