Superconvergence Analysis for Time-Fractional Diffusion Equations with Nonconforming Mixed Finite Element Method
Year: 2019
Author: Houchao Zhang, Dongyang Shi
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 4 : pp. 488–505
Abstract
In this paper, a fully discrete scheme based on the $L1$ approximation in temporal direction for the fractional derivative of order in (0, 1) and nonconforming mixed finite element method (MFEM) in spatial direction is established. First, we prove a novel result of the consistency error estimate with order $O(h^2)$ of $EQ^{rot}_1$ element (see Lemma 2.3). Then, by using the proved character of $EQ^{rot}_1$ element, we present the superconvergent estimates for the original variable $u$ in the broken $H^1$-norm and the flux $\vec{q} = ∇u$ in the $(L^2)^2$-norm under a weaker regularity of the exact solution. Finally, numerical results are provided to confirm the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1805-m2017-0256
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 4 : pp. 488–505
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Nonconforming MFEM $L1$ method Time-fractional diffusion equations Superconvergence.