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...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Sokolowski, Jan
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
Descripción
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.