Galerkin finite element method for higher dimensional multi-term fractional diffusion equation on non-uniform meshes. Issue 8 (11th June 2017)

• Record Type: Journal Article
• Authors: Li, Meng; Huang, Chengming; Jiang, Fengze
• Is Part Of: Applicable analysis. Volume 96:Issue 8(2017)
• Page Start: 1269
• Page End: 1284
• Publication Date: 2017-06-11
• Subjects: Fractional diffusion equation -- non-uniform meshes -- Galerkin finite element method -- stability analysis -- error estimates; 97N40 -- 65D07 -- 74S05 -- 26A33 -- 34A08 -- 65L60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1186271
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we study Galerkin finite element methods for a class of higher dimensional multi-term fractional diffusion equations. The finite difference approximation of Caputo derivative on non-uniform meshes is used in temporal direction and Galerkin finite element method is used in spatial direction. We prove that semi-discrete and fully discrete finite element schemes are unconditionally stable. Meanwhile, -norm convergence properties of the two schemes are proved rigorously. To confirm our theoretical analysis, we give some numerical examples in both two-dimensional (2D) and three-dimensional (3D) spaces. Finally, a moving local refinement technique in temporal direction is used to improve the accuracy of numerical solution.