Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains

JOURNAL OF COMPUTATIONAL PHYSICS

卷:330

Article

Yang, Z.¹  Yuan, Z.¹  Nie, Y.¹  Wang, J.¹  Zhu, X.¹  Liu, F.² 

[1] Northwestern Polytech Univ, Res Ctr Computat Sci, Xian 710072, Peoples R China

[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

关键词: Finite element method;    Riesz fractional derivative;    Nonlinear source term;    Irregular domain;   

DOI  :  10.1016/j.jcp.2016.10.053

来源: Elsevier

【 摘 要 】

In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free