On linear-quadratic elliptic control problems of semi-infinite type

摘要

We derive a priori error estimates for linear-quadratic elliptic optimal control problems with pointwise state constraints in a compact subdomain of the spatial domain Ω for a class of problems with finite-dimensional control space. The problem formulation leads to a class of semi-infinite programming problems, whose constraints are implicitly given by the FE-discretization of the underlying PDEs. We prove an order of h(|log h|)~(1/2) for the error |u{top}-(u{top}-)~h| in the controls, and show that it can be improved to an order of h~2|log h| under certain assumptions on the structure of the active set. Numerical experiments underline the proven theoretical results.