A Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations

被引：45
|
作者：
Wang, Hong [1 ]
Yang, Danping [2 ,3 ]
Zhu, Shengfeng [2 ,3 ]
机构：
[1] Univ S Carolina, Dept Math, Columbia, SC 29208 USA
[2] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
[3] E China Normal Univ, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2015年 / 290卷
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
Discontinuous Petrov-Galerkin framework; Fractional diffusion equations; Petrov-Galerkin finite element method; Weak coercivity; CIRCULANT PRECONDITIONER; DIFFERENCE METHOD; LEVY MOTION; DISPERSION; ELASTICITY; TURBULENCE; CALCULUS;
D O I：
10.1016/j.cma.2015.02.027
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
Fractional diffusion equations have found increasingly more applications in recent years but introduce new mathematical and numerical difficulties. Galerkin formulation, which was proved to be coercive and well-posed for fractional diffusion equations with a constant diffusivity coefficient, may lose its coercivity for variable-coefficient problems. The corresponding finite element method fails to converge. We utilize the discontinuous Petrov-Galerkin (DPG) framework to develop a Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations. We prove the well-posedness and optimal-order convergence of the Petrov-Galerkin finite element method. Numerical examples are presented to verify the theoretical results. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码：45 / 56
页数：12
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