Finite Element Method for a Kind of Two-Dimensional Space-Fractional Diffusion Equation with Its Implementation  

作　　者：Beiping Duan Zhoushun Zheng Wen Cao 

机构地区：[1]School of Mathematics and Statistics, Central South University, Changsha, China

出　　处：《American Journal of Computational Mathematics》2015年第2期135-157,共23页美国计算数学期刊（英文）

摘　　要：In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The stability and convergence are proved and the stiffness matrix is given analytically. Three numerical examples are given to confirm our theoretical analysis in which we find that even with the same initial condition, the classical and fractional diffusion equations perform differently but tend to be uniform diffusion at last.In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The stability and convergence are proved and the stiffness matrix is given analytically. Three numerical examples are given to confirm our theoretical analysis in which we find that even with the same initial condition, the classical and fractional diffusion equations perform differently but tend to be uniform diffusion at last.

关 键 词：GALERKIN Finite Element Method SYMMETRIC Space-Fractional Diffusion Equation Stability Convergence IMPLEMENTATION 

分 类 号：O1[理学—数学]