Taiwanese Journal of Mathematics

Superconvergence of FEM for Distributed Order Time Fractional Variable Coefficient Diffusion Equations

Yanhua Yang and Jincheng Ren

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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.

Article information

Taiwanese J. Math., Volume 22, Number 6 (2018), 1529-1545.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65N15: Error bounds 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

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


Yang, Yanhua; Ren, Jincheng. Superconvergence of FEM for Distributed Order Time Fractional Variable Coefficient Diffusion Equations. Taiwanese J. Math. 22 (2018), no. 6, 1529--1545. doi:10.11650/tjm/180606. https://projecteuclid.org/euclid.twjm/1531382428

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