Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional
Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise lin...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/2962 |
| Acceso en línea: | http://hdl.handle.net/10902/2962 |
| Access Level: | acceso abierto |
| Palabra clave: | Optimal control of partial differential equations Nondifferentiable objective Sparse controls Finite element discretization A priori error estimates |
| Sumario: | Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise linear discretizations of the state are shown. Error estimates for the variational discretization of the problem in the sense of [M. Hinze, Comput. Optim. Appl., 30 (2005), pp. 45--61] are also obtained. Numerical experiments confirm the convergence rates. |
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