Abstract
Abstract We consider the finite element discretization of an optimal Dirichlet boundary control problem for the Laplacian, where the control is considered in H 1 / 2 ( Γ ) {H^{1/2}(\Gamma)} . To avoid computing the latter norm numerically, we realize it using the H 1 ( Ω ) {H^{1}(\Omega)} norm of the harmonic extension of the control. We propose a mixed finite element discretization, where the harmonicity of the solution is included by a Lagrangian multiplier. In the case of convex polygonal domains, optimal error estimates in the H 1 {H^{1}} and L 2 {L_{2}} norm are proven. We also consider and analyze the case of control constrained problems.
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