Year: 2020
Author: Wenping Yuan, Yanping Chen, Yunqing Huang
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 818–837
Abstract
A local discontinuous Galerkin finite element method for a class of time-fractional Burgers equations is developed. In order to achieve a high order accuracy, the time-fractional Burgers equation is transformed into a first order system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. The scheme is proved to be unconditionally stable and in linear case it has convergence rate $\mathcal{O}$(τ2−α + $h$$k$+1), where $k$ ≥ 0 denotes the order of the basis functions used. Numerical examples demonstrate the efficiency and accuracy of the scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.300919.240520
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 818–837
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Time-fractional Burgers equation Caputo fractional derivative local discontinuous Galerkin method stability convergence.
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