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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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/9398265 |
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| author | Suxiang Yang Huanzhen Chen |
| author_facet | Suxiang Yang Huanzhen Chen |
| author_sort | Suxiang Yang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-64b6f786bfed4248879bc8c2bb2ed049 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-64b6f786bfed4248879bc8c2bb2ed0492025-02-03T06:46:26ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/93982659398265A Mixed Finite Element Formulation for the Conservative Fractional Diffusion EquationsSuxiang Yang0Huanzhen Chen1School of Mathematical Sciences, Shandong Normal University, Jinan 250014, ChinaSchool of Mathematical Sciences, Shandong Normal University, Jinan 250014, ChinaWe 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.http://dx.doi.org/10.1155/2016/9398265 |
| spellingShingle | Suxiang Yang Huanzhen Chen A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations Advances in Mathematical Physics |
| title | A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations |
| title_full | A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations |
| title_fullStr | A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations |
| title_full_unstemmed | A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations |
| title_short | A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations |
| title_sort | mixed finite element formulation for the conservative fractional diffusion equations |
| url | http://dx.doi.org/10.1155/2016/9398265 |
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