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Finite element approximation of Dirichlet boundary control for elliptic PDEs on two-and threedimensional curved domains

by Deckelnick, K., Guenther, A., Hinze, M..

Series: 2008-16, Preprints

49J20 Optimal control problems involving partial differential equations
49K20 Problems involving partial differential equations

We consider the variational discretization of elliptic Dirichlet optimal control problems with constraints on the control. The underlying state equation, which is considered on smooth two- and three-dimensional domains, is discretized
by linear finite elements taking into account domain approximation. The control variable is not discretized. We obtain optimal error bounds for the optimal control in two and three space dimensions and prove a superconvergence result in two dimensions provided that the underlying mesh satisfies some additional condition. We confirm our analytical findings by numerical experiments.

Elliptic optimal control problem, boundary control, control constraints, error estimates