Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality
The objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy g. The existence and uniquenes...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2015/407930 |
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| _version_ | 1849308104209989632 |
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| author | Mariela Olguín Domingo A. Tarzia |
| author_facet | Mariela Olguín Domingo A. Tarzia |
| author_sort | Mariela Olguín |
| collection | DOAJ |
| description | The objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy g. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positive h (the parameter of the finite element method approximation). Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameter h goes to zero. |
| format | Article |
| id | doaj-art-13c0099ddc9f42c6a56bab2d07e76ffc |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-13c0099ddc9f42c6a56bab2d07e76ffc2025-08-20T03:54:33ZengWileyInternational Journal of Differential Equations1687-96431687-96512015-01-01201510.1155/2015/407930407930Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational InequalityMariela Olguín0Domingo A. Tarzia1Departamento de Matemática, EFB-FCEIA, Universidad Nacional de Rosario, Avenida Pellegrini 250, S2000BPT Rosario, ArgentinaDepartamento de Matemática-CONICET, FCE, Universidad Austral, Paraguay 1950, S2000FZF Rosario, ArgentinaThe objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy g. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positive h (the parameter of the finite element method approximation). Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameter h goes to zero.http://dx.doi.org/10.1155/2015/407930 |
| spellingShingle | Mariela Olguín Domingo A. Tarzia Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality International Journal of Differential Equations |
| title | Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality |
| title_full | Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality |
| title_fullStr | Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality |
| title_full_unstemmed | Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality |
| title_short | Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality |
| title_sort | numerical analysis of a distributed optimal control problem governed by an elliptic variational inequality |
| url | http://dx.doi.org/10.1155/2015/407930 |
| work_keys_str_mv | AT marielaolguin numericalanalysisofadistributedoptimalcontrolproblemgovernedbyanellipticvariationalinequality AT domingoatarzia numericalanalysisofadistributedoptimalcontrolproblemgovernedbyanellipticvariationalinequality |