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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: .

(This article belongs to the 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.

## Keywords

APA Style
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. Computer Modeling in Engineering & Sciences, 122(3), 1081-1098. https://doi.org/10.32604/cmes.2020.07822
Vancouver Style
Zhang Y, Yin B, Cao Y, Liu Y, Li H. A numerical algorithm based on quadratic finite element for two-dimensional nonlinear time fractional thermal diffusion model. Comput Model Eng Sci. 2020;122(3):1081-1098 https://doi.org/10.32604/cmes.2020.07822
IEEE Style
Y. Zhang, B. Yin, Y. Cao, Y. Liu, and H. Li "A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model," Comput. Model. Eng. Sci., vol. 122, no. 3, pp. 1081-1098. 2020. https://doi.org/10.32604/cmes.2020.07822

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