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    Approximation of boundary control problems on curved domains

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    Identificadores
    URI: http://hdl.handle.net/10902/1629
    DOI: 10.1137/090761550
    ISSN: 1095-7138
    ISSN: 0363-0129
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    Author
    Casas Rentería, EduardoAutoridad Unican; Sokolowski, Jan
    Date
    2010
    Derechos
    © 2010 Society for Industrial and Applied Mathematics
    Publicado en
    Siam Journal on Control and Optimization, 2010, 48(6), 3746–3780
    Publisher
    Society for Industrial and Applied Mathematics
    Palabras clave
    Neumann control
    Dirichlet control
    Curved domains
    Error estimates
    Semilinear elliptic equations
    Second order optimality conditions
    Abstract:
    In this paper we consider boundary control problems associated to a semilinear elliptic equation defined in a curved domain Ω. The Dirichlet and Neumann cases are analyzed. To deal with the numerical analysis of these problems, the approximation of Ω by an appropriate domain Ωh (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 Ωh, and we study the influence of the replacement of Ω by Ωh on the solutions of the control problems. Our goal is to compare the optimal controls defined on Γ = ∂Ω with those defined on Γh = ∂Ωh and to derive some error estimates. The use of a convenient parametrization of the boundary is needed for such estimates.
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    • D20 Artículos [340]

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    UNIVERSIDAD DE CANTABRIA

    Repositorio realizado por la Biblioteca Universitaria utilizando DSpace software
    Contact Us | Send Feedback
    Metadatos sujetos a:licencia de Creative Commons Reconocimiento 3.0 España