Multigrid methods for space fractional partial differential equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:302

Article

Jiang, Yingjun¹  Xu, Xuejun^2,3 

[1] Changsha Univ Sci & Technol, Dept Math & Sci Comp, Changsha 410076, Hunan, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China

[3] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

关键词: Fractional differential equations;    Multigrid methods;    Optimal convergence;   

DOI  :  10.1016/j.jcp.2015.08.052

来源: Elsevier

【 摘 要 】

We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means the convergence rates of the methods are independent of the mesh size and mesh level, Moreover, our theoretical analysis and convergence results do not require regularity assumptions of the model problems. Numerical results are given to support our theoretical findings. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free