Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations
We focus on developing the finite difference (i.e., backward Euler difference or second-order central difference)/local discontinuous Galerkin finite element mixed method to construct and analyze a kind of efficient, accurate, flexible, numerical schemes for approximately solving time-space fraction...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/4961797 |
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| author | Meilan Qiu Liquan Mei Dewang Li |
| author_facet | Meilan Qiu Liquan Mei Dewang Li |
| author_sort | Meilan Qiu |
| collection | DOAJ |
| description | We focus on developing the finite difference (i.e., backward Euler difference or second-order central difference)/local discontinuous Galerkin finite element mixed method to construct and analyze a kind of efficient, accurate, flexible, numerical schemes for approximately solving time-space fractional subdiffusion/superdiffusion equations. Discretizing the time Caputo fractional derivative by using the backward Euler difference for the derivative parameter (0<α<1) or second-order central difference method for (1<α<2), combined with local discontinuous Galerkin method to approximate the spatial derivative which is defined by a fractional Laplacian operator, two high-accuracy fully discrete local discontinuous Galerkin (LDG) schemes of the time-space fractional subdiffusion/superdiffusion equations are proposed, respectively. Through the mathematical induction method, we show the concrete analysis for the stability and the convergence under the L2 norm of the LDG schemes. Several numerical experiments are presented to validate the proposed model and demonstrate the convergence rate of numerical schemes. The numerical experiment results show that the fully discrete local discontinuous Galerkin (LDG) methods are efficient and powerful for solving fractional partial differential equations. |
| format | Article |
| id | doaj-art-2c41b326954741ad9e8560e12fc8d5b7 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-2c41b326954741ad9e8560e12fc8d5b72025-02-03T06:47:25ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/49617974961797Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion EquationsMeilan Qiu0Liquan Mei1Dewang Li2School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaDepartment of Mathematics, Huizhou University, Huizhou, Guangdong 516007, ChinaWe focus on developing the finite difference (i.e., backward Euler difference or second-order central difference)/local discontinuous Galerkin finite element mixed method to construct and analyze a kind of efficient, accurate, flexible, numerical schemes for approximately solving time-space fractional subdiffusion/superdiffusion equations. Discretizing the time Caputo fractional derivative by using the backward Euler difference for the derivative parameter (0<α<1) or second-order central difference method for (1<α<2), combined with local discontinuous Galerkin method to approximate the spatial derivative which is defined by a fractional Laplacian operator, two high-accuracy fully discrete local discontinuous Galerkin (LDG) schemes of the time-space fractional subdiffusion/superdiffusion equations are proposed, respectively. Through the mathematical induction method, we show the concrete analysis for the stability and the convergence under the L2 norm of the LDG schemes. Several numerical experiments are presented to validate the proposed model and demonstrate the convergence rate of numerical schemes. The numerical experiment results show that the fully discrete local discontinuous Galerkin (LDG) methods are efficient and powerful for solving fractional partial differential equations.http://dx.doi.org/10.1155/2017/4961797 |
| spellingShingle | Meilan Qiu Liquan Mei Dewang Li Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations Advances in Mathematical Physics |
| title | Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations |
| title_full | Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations |
| title_fullStr | Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations |
| title_full_unstemmed | Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations |
| title_short | Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations |
| title_sort | fully discrete local discontinuous galerkin approximation for time space fractional subdiffusion superdiffusion equations |
| url | http://dx.doi.org/10.1155/2017/4961797 |
| work_keys_str_mv | AT meilanqiu fullydiscretelocaldiscontinuousgalerkinapproximationfortimespacefractionalsubdiffusionsuperdiffusionequations AT liquanmei fullydiscretelocaldiscontinuousgalerkinapproximationfortimespacefractionalsubdiffusionsuperdiffusionequations AT dewangli fullydiscretelocaldiscontinuousgalerkinapproximationfortimespacefractionalsubdiffusionsuperdiffusionequations |