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June, 2020 High Spatial Accuracy Analysis of Linear Triangular Finite Element for Distributed Order Diffusion Equations
Lin He, Jincheng Ren
Taiwanese J. Math. 24(3): 695-708 (June, 2020). DOI: 10.11650/tjm/190803

Abstract

In this paper, an effective numerical fully discrete finite element scheme for the distributed order time fractional diffusion equations is developed. By use of the composite trapezoid formula and the well-known $L1$ formula approximation to the distributed order derivative and linear triangular finite element approach for the spatial discretization, we construct a fully discrete finite element scheme. Based on the superclose estimate between the interpolation operator and the Ritz projection operator and the interpolation post-processing technique, the superclose approximation of the finite element numerical solution and the global superconvergence are proved rigorously, respectively. Finally, a numerical example is presented to support the theoretical results.

Citation

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Lin He. Jincheng Ren. "High Spatial Accuracy Analysis of Linear Triangular Finite Element for Distributed Order Diffusion Equations." Taiwanese J. Math. 24 (3) 695 - 708, June, 2020. https://doi.org/10.11650/tjm/190803

Information

Received: 28 March 2019; Revised: 17 July 2019; Accepted: 18 August 2019; Published: June, 2020
First available in Project Euclid: 19 May 2020

zbMATH: 07251193
MathSciNet: MR4100715
Digital Object Identifier: 10.11650/tjm/190803

Subjects:
Primary: 65N15, 65N30

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 3 • June, 2020
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