Displaying similar documents to “Penalization of Dirichlet optimal control problems”

Singular perturbation for the Dirichlet boundary control of elliptic problems

Faker Ben Belgacem, Henda El Fekih, Hejer Metoui (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for...

Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space

Pedro Merino, Fredi Tröltzsch, Boris Vexler (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.

Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems

Eduardo Casas, Fredi Tröltzsch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Optimal control problems for semilinear elliptic equations with control constraints and pointwise state constraints are studied. Several theoretical results are derived, which are necessary to carry out a numerical analysis for this class of control problems. In particular, sufficient second-order optimality conditions, some new regularity results on optimal controls and a sufficient condition for the uniqueness of the Lagrange multiplier associated with the state constraints are presented. ...

Penalization of Dirichlet optimal control problems

Eduardo Casas, Mariano Mateos, Jean-Pierre Raymond (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We apply Robin penalization to Dirichlet optimal control problems governed by semilinear elliptic equations. Error estimates in terms of the penalization parameter are stated. The results are compared with some previous ones in the literature and are checked by a numerical experiment. A detailed study of the regularity of the solutions of the PDEs is carried out.