Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
This is the first of two papers concerned with a state-constrained
optimal control problems with boundary control, where the state constraints
are only imposed in an interior subdomain. We apply the virtual control
concept introduced in [20] to regularize the problem. The arising regularized
optimal control problem is discretized by finite elements and linear and
continuous ansatz functions for the boundary control. In the first part of
the work, we investigate the errors induced by the regularization and the
discretization of the boundary control. The second part deals with the error
arising from discretization of the PDE. Since the state constraints only
appear in an inner subdomain, the obtained order of convergence exceeds the
known results in the field of a priori analysis for state-constrained
problem