Global superconvergence analysis of nonconforming finite element method for time fractional reaction-diffusion problem with anisotropic data

Abstract

In this paper, a class of two-dimensional (2-D) time fractional reaction-diffusion equation is considered. The solution usually exhibits singularity at the initial moment and anisotropic behavior in the spatial direction. In response to these problems, we provide an effective numerical framework for analyzing the L2-norm error, H1-norm superclose property and H1-norm global superconvergence result. This framework combines the high-precision L2-1σ scheme on non-uniform time grids and the anisotropic nonconforming quasi-Wilson finite element method (FEM) in space. Some numerical experiments are presented to illustrate our theoretical findings.