@Article{cmes.2020.07822, AUTHOR = {Yanlong Zhang, Baoli Yin, Yue Cao, Yang Liu , *, Hong Li}, TITLE = {A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model}, JOURNAL = {Computer Modeling in Engineering \& Sciences}, VOLUME = {122}, YEAR = {2020}, NUMBER = {3}, PAGES = {1081--1098}, URL = {http://www.techscience.com/CMES/v122n3/38393}, ISSN = {1526-1506}, 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.}, DOI = {10.32604/cmes.2020.07822} }