Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space
Department of Mathematics, EPN Quito, Ecuador.
2 Institut für Mathematik, TU Berlin, Germany. troeltz@math.TU-Berlin.DE
Revised: 16 July 2009
The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.
Mathematics Subject Classification: 49J20 / 35B37
Key words: Finite element approximation / optimal control problem / finitely many pointwise state constraints
© EDP Sciences, SMAI, 2009