Finite element approximation of fractional order elliptic boundary value problems

被引：10
|
作者：
Szekeres, Bela J. [1 ]
Izsak, Ferenc [1 ]
机构：
[1] Eotvos Lorand Univ, Dept Appl Anal & Computat Math, H-1117 Budapest, Hungary
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 292卷
基金：
匈牙利科学研究基金会;
关键词：
Fractional order Laplacian; Matrix transformation method; Finite element method; Error estimation; ANOMALOUS DIFFUSION; SPACE; SCHEME; VOLUME; EQUATIONS;
D O I：
10.1016/j.cam.2015.07.026
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页码：553 / 561
页数：9
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