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Approximation of boundary control problems on curved domains

Abstract: 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.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Autoría: Casas E., Sokolowski J.,

 Fuente: SIAM Journal on Control and Optimization, 2010, 48(6), 3746-3780

Editorial: Society for Industrial and Applied Mathematics

 Fecha de publicación: 01/03/2010

Nº de páginas: 35

Tipo de publicación: Artículo de Revista

 DOI: 10.1137/090761550

ISSN: 0363-0129,1095-7138

 Proyecto español: MTM2008-0420