On goal-oriented adaptivity for elliptic optimal control problems

An Introduction to the A Posteriori Error Analysis of Elliptic Optimal Control Problems

We aim at a survey on adaptive finite element methods for optimal control problems associated with second order elliptic boundary value problems. Both unconstrained and constrained problems will be considered, the latter in case of pointwise control and pointwise state constraints. Mesh adaptivity is realized in terms of a posteriori error estimators obtained by using residual-type error contro...

Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state

An adaptive finite element method is developed for a class of optimal control problems with elliptic variational inequality constraints and objective functionals defined on the space of continuous functions, necessitated by a point-tracking requirement with respect to the state variable. A suitable first order stationarity concept is derived for the problem class via a penalty technique. The du...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Goal-Oriented Adaptivity in Pointwise State Constrained Optimal Control of Partial Differential Equations

Primal-dual-weighted goal-oriented a posteriori error estimates for pointwise state constrained optimal control problems for second order elliptic partial differential equations are derived. The constraints give rise to a primal-dual weighted error term representing the mismatch in the complementarity system due to discretization. In the case of sufficiently regular active (or coincidence) sets...

Goal-oriented adaptive concepts for elliptic optimal control problems in the presence of control and state constraints