Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space

Merino, Pedro; Tröltzsch, Fredi; Vexler, Boris

ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 1, pp. 167-188.

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.

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