06-02
Convergence of a finite element approximation to a state constrained elliptic control problem
Preprint series: 06-02, Preprints
- MSC:
- 49J20 Optimal control problems involving partial differential equations
- 35B37 PDE in connection with control problems, See also {49J20, 49K20, 93C20}
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 both in two and three space dimensions. Furthermore, error bounds both for control and state are obtained in the two-dimensional case. Finally, we present numerical examples which confirm our analytical findings.
Keywords: elliptic optimal control problem, state contraints, error estimates
The author(s) agree, that this abstract may be stored asfull text and distributed as such by abstracting services.