Finite element approximation of fractional order elliptic boundary value problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:292

Article

Szekeres, Bela J.¹  Izsak, Ferenc¹ 

[1] Eotvos Lorand Univ, Dept Appl Anal & Computat Math, H-1117 Budapest, Hungary

关键词: Fractional order Laplacian;    Matrix transformation method;    Finite element method;    Error estimation;   

DOI  :  10.1016/j.cam.2015.07.026

来源: Elsevier

【 摘 要 】

A finite element numerical method is investigated for fractional order elliptic boundary value problems with homogeneous Dirichlet type boundary conditions. It is pointed out that an appropriate stiffness matrix can be obtained by taking the prescribed fractional power of the stiffness matrix corresponding to the non-fractional elliptic operators. It is proved that this approach, which is also called the matrix transformation or matrix transfer method, delivers optimal rate of convergence in the L-2-norm. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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