Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem

Authors:
Klaus Deckelnick;Michael Hinze
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2007

Citing 0
Cited 18

Error estimates for the discretization of elliptic control problems with pointwise control and state constraints

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A Priori Error Estimates for Finite Element Discretizations of Parabolic Optimization Problems with Pointwise State Constraints in Time

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Numerical approximation of elliptic control problems with finitely many pointwise constraints

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Stability of semilinear elliptic optimal control problems with pointwise state constraints

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Asymptotic Expansion for the Solutions of Control Constrained Semilinear Elliptic Problems with Interior Penalties

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A general theorem on error estimates with application to a quasilinear elliptic optimal control problem

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Optimal error estimates for finite element discretization of elliptic optimal control problems with finitely many pointwise state constraints

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Error estimates for parabolic optimal control problems with control and state constraints

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A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator

Calcolo: a quarterly on numerical analysis and theory of computation

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Abstract

We consider an elliptic optimal control problem with pointwise state constraints. The cost functional is approximated by a sequence of functionals which are obtained by discretizing the state equation with the help of linear finite elements and enforcing the state constraints in the nodes of the triangulation. The corresponding minima are shown to converge in $L^2$ to the exact control as the discretization parameter tends to zero. Furthermore, error bounds for the control and the state are obtained in both two and three space dimensions. Finally, we present numerical examples which confirm our analytical findings.