Displaying similar documents to “Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations”

On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider

Ionel Ciuperca, Mohamed El Alaoui Talibi, Mohammed Jai (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.

Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations

Eduardo Casas, Fredi Tröltzsch (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we carry out the numerical analysis of a distributed optimal control problem governed by a quasilinear elliptic equation of non-monotone type. The goal is to prove the strong convergence of the discretization of the problem by finite elements. The main issue is to get error estimates for the discretization of the state equation. One of the difficulties in this analysis is that, in spite of the partial differential equation has a unique solution for any given control,...

Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems

Pedro Merino, Ira Neitzel, Fredi Tröltzsch (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.

Error estimates for finite element approximations of elliptic control problems

Walter Alt, Nils Bräutigam, Arnd Rösch (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.

Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints

Eduardo Casas (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that...

Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity

E. Casas, O. Kavian, J.-P. Puel (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity, such that we cannot expect to have a solution of the state equation for any given control. We then have to speak of pairs (control, state). After having defined a suitable functional class in which we look for solutions, we prove existence of an optimal pair for a large class of cost functions using a non standard compactness argument. Then, we derive a first order optimality...