Yanlong Zhang1, Baoli Yin1, Yue Cao1, Yang Liu1 , *, Hong Li1
CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.3, pp. 1081-1098, 2020, DOI: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. More >
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