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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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

Taiwanese J. Math., Volume 24, Number 3 (2020), 695-708.

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

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

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


He, Lin; Ren, Jincheng. High Spatial Accuracy Analysis of Linear Triangular Finite Element for Distributed Order Diffusion Equations. Taiwanese J. Math. 24 (2020), no. 3, 695--708. doi:10.11650/tjm/190803. https://projecteuclid.org/euclid.twjm/1589875225

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