Open Access

ARTICLE

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

Yanlong Zhang¹, Baoli Yin¹, Yue Cao¹, Yang Liu^{1 , *}, 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

Received 22 July 2019; Accepted 20 August 2019; Issue published 01 March 2020

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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Keywords

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