High Accuracy Analysis of an Anisotropic Nonconforming Finite Element Method for Two-Dimensional Time Fractional Wave Equation

Abstract

High-order numerical analysis of a nonconforming finite element method on regular and anisotropic meshes for two dimensional time fractional wave equation is presented. The stability of a fully-discrete approximate scheme based on quasi-Wilson FEM in spatial direction and Crank-Nicolson approximation in temporal direction is proved and spatial global superconvergence and temporal convergence order $\mathcal{O}$($h$² + τ^3−$α$) in the broken $H$¹-norm is established. For regular and anisotropic meshes, numerical examples are consistent with theoretical results.