A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient

摘要

Based on the spatial quasi-Wilson nonconforming finite element method and temporal L2 - 1(sigma) , formula, a fully-discrete approximate scheme is proposed for a two-dimensional time-fractional diffusion equations with variable coefficient on anisotropic meshes. In order to demonstrate the stable analysis and error estimates, several lemmas are provided, which focus on high accuracy about projection and superclose estimate between the interpolation and projection. Unconditionally stable analysis are derived in L-2-norm and broken H-1-norm. Moreover, convergence result of accuracy O(h(2) + tau(2)) and superclose property of accuracy O(h(2) + tau(2)) are deduced by combining interpolation with projection, where h and tau are the step sizes in space and time, respectively. And then, the global superconvergence is presented by employing interpolation post processing operator. Finally, numerical results are provided to demonstrate the validity of the theoretical analysis. (C) 2018 Elsevier Ltd. All rights reserved.