Finite element approximation of fractional order elliptic boundary value problems

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 corres...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-01, Vol.292, p.553-561
Main Authors: Szekeres, Béla J., Izsák, Ferenc
Format: Article
Language:English
Subjects:
Approximation
Boundary value problems
Convergence
Dirichlet problem
Error estimation
Finite element method
Fractional order Laplacian
Mathematical analysis
Matrix transformation method
Stiffness matrix
Transformations
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Summary: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 L2-norm.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.07.026