Vol.122, No.3, 2020, pp.1081-1098, doi:10.32604/cmes.2020.07822
OPEN ACCESS
RESEARCH 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 Liu1 , *, Hong Li1
1 School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China.
∗ Corresponding Author: Yang Liu. Email: mathliuyang@imu.edu.cn.
(This article belongs to this Special Issue: Numerical Methods for Differential and Integral Equations)
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.
Keywords
Quadratic finite element, two-dimensional nonlinear time fractional thermal diffusion model, L2 -1 σ formula.
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.