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December, 2018 Superconvergence of FEM for Distributed Order Time Fractional Variable Coefficient Diffusion Equations
Yanhua Yang, Jincheng Ren
Taiwanese J. Math. 22(6): 1529-1545 (December, 2018). DOI: 10.11650/tjm/180606

Abstract

In this paper, a numerical fully discrete scheme based on the finite element approximation for the distributed order time fractional variable coefficient diffusion equations is developed and a complete error analysis is provided. The weighted and shifted Grünwald formula is applied for the time-fractional derivative and finite element approach for the spatial discretization. The unconditional stability and the global superconvergence estimate of the fully discrete scheme are proved rigorously. Extensive numerical experiments are presented to illustrate the accuracy and efficiency of the scheme, and to verify the convergence theory.

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Yanhua Yang. Jincheng Ren. "Superconvergence of FEM for Distributed Order Time Fractional Variable Coefficient Diffusion Equations." Taiwanese J. Math. 22 (6) 1529 - 1545, December, 2018. https://doi.org/10.11650/tjm/180606

Information

Received: 7 December 2017; Revised: 15 May 2018; Accepted: 19 June 2018; Published: December, 2018
First available in Project Euclid: 12 July 2018

zbMATH: 07021703
MathSciNet: MR3880239
Digital Object Identifier: 10.11650/tjm/180606

Subjects:
Primary: 65N15 , 65N30

Keywords: distributed order diffusion equations , finite element method , fully discrete scheme , superconvergence estimate

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

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Vol.22 • No. 6 • December, 2018
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