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Superconvergence Analysis for Time-Fractional Diffusion Equations with Nonconforming Mixed Finite Element Method

Superconvergence Analysis for Time-Fractional Diffusion Equations with Nonconforming Mixed Finite Element Method
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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.

Author Details

Houchao Zhang

Dongyang Shi

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