Approximation of boundary control problems on curved domains
In this paper we consider boundary control problems associated to a semilinear elliptic equation defined in a curved domain [omega]. The Dirichlet and Neumann cases are analyzed. To deal with the numerical analysis of these problems, the approximation of [omega] by an appropriate domain [omega]h (ty...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/26711 |
| Acceso en línea: | https://hdl.handle.net/10902/26711 |
| Access Level: | acceso abierto |
| Palabra clave: | Neumann control Dirichlet control Curved domains Error estimates Semilinearelliptic equations Second order optimality condition |
| Sumario: | In this paper we consider boundary control problems associated to a semilinear elliptic equation defined in a curved domain [omega]. The Dirichlet and Neumann cases are analyzed. To deal with the numerical analysis of these problems, the approximation of [omega] by an appropriate domain [omega]h (typically polygonal) is required. Here we do not consider the numerical approximation of the control problems. Instead, we formulate the corresponding infinite dimensional control problems in [omega]h, and we study the influence of the replacement of [omega] by [omega]h on the solutions of the control problems. Our goal is to compare the optimal controls defined on T=e[omega] with those defined on Th=e[omega]h and to derive some error estimates. The use of a convenient parametrization of the boundary is needed for such estimates. |
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