Leapfrog/Finite Element Method for Fractional Diffusion Equation

We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discuss...

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Bibliographic Details
Main Authors: Zhengang Zhao, Yunying Zheng
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2014/982413
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Summary:We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L2-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis.
ISSN:2356-6140
1537-744X