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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Apel, T., Rösch, A. & Winkler, G. Optimal control in non-convex domains: a priori discretization error estimates. Calcolo 44, 137–158 (2007). https://doi.org/10.1007/s10092-007-0133-0
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DOI: https://doi.org/10.1007/s10092-007-0133-0