Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints

• Autorzy: Meyer C.
• Języki publikacji: EN

Abstrakty

EN

We consider a linear-quadratic elliptic optimal control problem with pointwise state constraints. The problem is fully discretized using linear ansatz functions for state and control. Based on a Slater-type argument, we investigate the approximation behavior for mesh size tending to zero. The obtained convergence order for the L²-error of the control and for H 1-error of the state is 1 - ε in the two-dimensional case and 1/2 - ε in three dimensions, provided that the domain satisfies certain regularity assumptions. In a second step, a state-constrained problem with additional control constraints is considered. Here, the control is discretized by constant ansatz functions. It is shown that the convergence theory can be adapted to this case yielding the same order of convergence. The theoretical findings are confirmed by numerical examples.

Słowa kluczowe

EN

linear quadratic optimal control problems; elliptic equations; state constraints; numerical approximation

PL

równanie eliptyczne; aproksymacja numeryczna

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2008
• Tom: Vol. 37, no 1
• Strony: 51--83
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Meyer C.

• Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin, Germany

Bibliografia

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