Abstract

We consider the Galerkin finite element approximation of an elliptic Dirichlet boundary control model problem governed by the Laplacian operator. The analytical setting of this problem uses $L^2$ controls and a “very weak” formulation of the state equation. However, the corresponding finite element approximation uses standard continuous trial and test functions. For this approximation, we derive a priori error estimates of optimal order, which are confirmed by numerical experiments. The proofs employ duality arguments and known results from the $L^p$ error analysis for the finite element Dirichlet projection.

Keywords

  1. Dirichlet boundary control
  2. finite elements
  3. a priori error estimates

MSC codes

  1. 65K10
  2. 65N30
  3. 65N21
  4. 49M25
  5. 49K20

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Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 2585 - 2611
ISSN (online): 1095-7138

History

Submitted: 19 September 2008
Accepted: 18 March 2013
Published online: 25 June 2013

Keywords

  1. Dirichlet boundary control
  2. finite elements
  3. a priori error estimates

MSC codes

  1. 65K10
  2. 65N30
  3. 65N21
  4. 49M25
  5. 49K20

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