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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(h2) of EQrot1 element (see Lemma 2.3). Then, by using the proved character of EQrot1 element, we present the superconvergent estimates for the original variable u in the broken H1-norm and the flux →q=∇u in the (L2)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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