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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/982413 |
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| _version_ | 1850177616839966720 |
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| author | Zhengang Zhao Yunying Zheng |
| author_facet | Zhengang Zhao Yunying Zheng |
| author_sort | Zhengang Zhao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b9deafef458b42f9bf509e32e78c0397 |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-b9deafef458b42f9bf509e32e78c03972025-08-20T02:18:57ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/982413982413Leapfrog/Finite Element Method for Fractional Diffusion EquationZhengang Zhao0Yunying Zheng1Department of Fundamental Courses, Shanghai Customs College, Shanghai 201204, ChinaSchool of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, ChinaWe 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.http://dx.doi.org/10.1155/2014/982413 |
| spellingShingle | Zhengang Zhao Yunying Zheng Leapfrog/Finite Element Method for Fractional Diffusion Equation The Scientific World Journal |
| title | Leapfrog/Finite Element Method for Fractional Diffusion Equation |
| title_full | Leapfrog/Finite Element Method for Fractional Diffusion Equation |
| title_fullStr | Leapfrog/Finite Element Method for Fractional Diffusion Equation |
| title_full_unstemmed | Leapfrog/Finite Element Method for Fractional Diffusion Equation |
| title_short | Leapfrog/Finite Element Method for Fractional Diffusion Equation |
| title_sort | leapfrog finite element method for fractional diffusion equation |
| url | http://dx.doi.org/10.1155/2014/982413 |
| work_keys_str_mv | AT zhengangzhao leapfrogfiniteelementmethodforfractionaldiffusionequation AT yunyingzheng leapfrogfiniteelementmethodforfractionaldiffusionequation |