A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem
In this paper, we investigate a mixed discontinuous Galerkin approximation of time dependent convection diffusion optimal control problem with control constraints based on the combination of a mixed finite element method for the elliptic part and a discontinuous Galerkin method for the hyperbolic pa...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/6901467 |
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| _version_ | 1832558677820702720 |
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| author | Qingjin Xu Zhaojie Zhou |
| author_facet | Qingjin Xu Zhaojie Zhou |
| author_sort | Qingjin Xu |
| collection | DOAJ |
| description | In this paper, we investigate a mixed discontinuous Galerkin approximation of time dependent convection diffusion optimal control problem with control constraints based on the combination of a mixed finite element method for the elliptic part and a discontinuous Galerkin method for the hyperbolic part of the state equation. The control variable is approximated by variational discretization approach. A priori error estimates of the state, adjoint state, and control are derived for both semidiscrete scheme and fully discrete scheme. Numerical example is given to show the effectiveness of the numerical scheme. |
| format | Article |
| id | doaj-art-aa4451dd08064cd9a0c8bac651163422 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-aa4451dd08064cd9a0c8bac6511634222025-02-03T01:31:47ZengWileyJournal of Mathematics2314-46292314-47852017-01-01201710.1155/2017/69014676901467A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control ProblemQingjin Xu0Zhaojie Zhou1College of Mathematical Sciences, Shandong Normal University, Jinan, ChinaCollege of Mathematical Sciences, Shandong Normal University, Jinan, ChinaIn this paper, we investigate a mixed discontinuous Galerkin approximation of time dependent convection diffusion optimal control problem with control constraints based on the combination of a mixed finite element method for the elliptic part and a discontinuous Galerkin method for the hyperbolic part of the state equation. The control variable is approximated by variational discretization approach. A priori error estimates of the state, adjoint state, and control are derived for both semidiscrete scheme and fully discrete scheme. Numerical example is given to show the effectiveness of the numerical scheme.http://dx.doi.org/10.1155/2017/6901467 |
| spellingShingle | Qingjin Xu Zhaojie Zhou A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem Journal of Mathematics |
| title | A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem |
| title_full | A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem |
| title_fullStr | A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem |
| title_full_unstemmed | A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem |
| title_short | A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem |
| title_sort | mixed discontinuous galerkin approximation of time dependent convection diffusion optimal control problem |
| url | http://dx.doi.org/10.1155/2017/6901467 |
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