Taiwanese Journal of Mathematics

High Spatial Accuracy Analysis of Linear Triangular Finite Element for Distributed Order Diffusion Equations

Lin He and Jincheng Ren

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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.

Article information

Source
Taiwanese J. Math., Advance publication (2019), 14 pages.

Dates
First available in Project Euclid: 21 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1566352830

Digital Object Identifier
doi:10.11650/tjm/190803

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

Keywords
distributed order diffusion equations the $L1$ formula linear triangular finite element superclose and superconvergence estimates

Citation

He, Lin; Ren, Jincheng. High Spatial Accuracy Analysis of Linear Triangular Finite Element for Distributed Order Diffusion Equations. Taiwanese J. Math., advance publication, 21 August 2019. doi:10.11650/tjm/190803. https://projecteuclid.org/euclid.twjm/1566352830


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