Optimal control in non-convex domains: a priori discretization error estimates |
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Authors: | Thomas Apel Arnd Rösch Gunter Winkler |
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Affiliation: | 1.Institut für Mathematik und Bauinformatik, Fakult?t für Bauingenieur- und Vermessungswesen, Universit?t der Bundeswehr München, 85577 Neubiberg,Germany;2.A. R?sch Fachbereich Mathematik, Universit?t Duisburg-Essen, Forsthausweg 2, 47057 Duisburg,Germany |
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Abstract: | Abstract An optimal control problem for a two-dimensional elliptic equation with pointwise control constraints is investigated. The domain is assumed to be polygonal but non-convex. The corner singularities are treated by a priori mesh grading. Approximations of the optimal solution of the continuous optimal control problem are constructed by a projection of the discrete adjoint state. It is proved that these approximations have convergence order h2. Keywords Linear-quadratic optimal control problems, error estimates, elliptic equations, non-convex domains, corner singularities, control constraints, superconvergence. Mathematics Subject Classification (2000): 49K20, 49M25, 65N30, 65N50 |
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