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A Finite Element Method for Elliptic Dirichlet Boundary Control Problems

  • Michael Karkulik EMAIL logo


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 ) . To avoid computing the latter norm numerically, we realize it using the H 1 ( Ω ) 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 and L 2 norm are proven. We also consider and analyze the case of control constrained problems.

MSC 2010: 65N30

Award Identifier / Grant number: 1170672

Funding statement: Supported by CONICYT through FONDECYT project 1170672.


The author would like to thank his colleagues Alejandro Allendes and Enrique Otárola for fruitful discussions.


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Received: 2019-07-02
Revised: 2020-06-08
Accepted: 2020-06-17
Published Online: 2020-08-05
Published in Print: 2020-10-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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