Superconvergence analysis of nonconforming finite element method for time-fractional nonlinear parabolic equations on anisotropic meshes

摘要

In this paper, we prove a novel result of the consistency error estimate with order O(h(2)) for EQ(1)(rot) element (see Lemma 2) on anisotropic meshes. Then, a linearized fully discrete Galerkin finite element method (FEM) is studied for the time-fractional nonlinear parabolic problems, and the superclose and superconvergent estimates of order O(tau + h(2)) in broken H-1-norm on anisotropic meshes are derived by using the proved character of EQ(1)(rot) element, which improve the results in the existing literature. Numerical results are provided to confirm the theoretical analysis. Published by Elsevier Ltd.