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A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

Yanlong Zhang1, Baoli Yin1, Yue Cao1, Yang Liu1 , *, Hong Li1

1 School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China.

∗ Corresponding Author: Yang Liu. Email: email.

(This article belongs to this Special Issue: Numerical Methods for Differential and Integral Equations)

Computer Modeling in Engineering & Sciences 2020, 122(3), 1081-1098. https://doi.org/10.32604/cmes.2020.07822

Abstract

In this article, a high-order scheme, which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme, is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model. The time Caputo fractional derivative is approximated by using the L2 -1 σ formula, the first-order derivative and nonlinear term are discretized by some second-order approximation formulas, and the quadratic finite element is used to approximate the spatial direction. The error accuracy O(h 3 + ∆t 2 ) is obtained, which is verified by the numerical results.

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Cite This Article

Zhang, Y., Yin, B., Cao, Y., Liu, Y., Li, H. (2020). A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model. CMES-Computer Modeling in Engineering & Sciences, 122(3), 1081–1098. https://doi.org/10.32604/cmes.2020.07822



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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