- Tytuł:
- Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints
- Autorzy:
- Meyer, C.
- Powiązania:
- https://bibliotekanauki.pl/articles/971011.pdf
- Data publikacji:
- 2008
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
równanie eliptyczne
aproksymacja numeryczna
linear quadratic optimal control problems
elliptic equations
state constraints
numerical approximation - Opis:
- 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.
- Źródło:
-
Control and Cybernetics; 2008, 37, 1; 51-83
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł