A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations

We consider a boundary-value problem of one-side conservative elliptic equation involving Riemann-Liouville fractional integral. The appearance of the singular term in the solution leads to lower regularity of the solution of the equation, so to the lower order convergence rate for the numerical sol...

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Bibliographic Details
Published in:Advances in mathematical physics 2016-01, Vol.2016 (2016), p.1-11
Main Authors: Yang, Suxiang, Chen, Huan-zhen
Format: Article
Language:English
Subjects:
Diffusion
Finite element analysis
Finite volume method
Numerical analysis
Partial differential equations
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Summary:We consider a boundary-value problem of one-side conservative elliptic equation involving Riemann-Liouville fractional integral. The appearance of the singular term in the solution leads to lower regularity of the solution of the equation, so to the lower order convergence rate for the numerical solution. In this paper, by the dividing of equation, we drop the lower regularity term in the solution successfully and get a new fractional elliptic equation which has full regularity. We present a theoretical framework of mixed finite element approximation to the new fractional elliptic equation and derive the error estimates for unknown function, its derivative, and fractional-order flux. Some numerical results are illustrated to confirm the optimal error estimates.
ISSN:1687-9120
1687-9139
DOI:10.1155/2016/9398265