High-order local discontinuous Galerkin method combined with WSGD-approximation for a fractional subdiffusion equation
Document Type
Article
Publication Date
1-1-2017
Publication Title
Computers and Mathematics with Applications
Volume
73
Issue
6
First page number:
1298
Last page number:
1314
Abstract
In this paper, a high-order local discontinuous Galerkin (LDG) method combined with weighted and shifted Grünwald difference (WSGD) approximation is developed and discussed for a Caputo time-fractional subdiffusion equation. The time fractional derivative of order α, 0>α>1, is approximated by a third-order method based on the idea of WSGD operator, while the spatial operator is approximated by the LDG method. Some useful lemmas are first introduced and proved, then the analysis of stability and optimal error estimate O(Δt3+hk+1) are obtained for the LDG method. Extensive numerical results using Pk,k=0,1,2,3, elements are presented to validate our theoretical analysis. © 2016 Elsevier Ltd
Language
english
Repository Citation
Liu, Y.,
Zhang, M.,
Li, H.,
Li, J.
(2017).
High-order local discontinuous Galerkin method combined with WSGD-approximation for a fractional subdiffusion equation.
Computers and Mathematics with Applications, 73(6),
1298-1314.
http://dx.doi.org/10.1016/j.camwa.2016.08.015