A priori error analysis for state constrained boundary control problems. Part I: Control discretization
- Krumbiegel, Klaus
- Meyer, Christian
- Rösch, Arnd
2010 Mathematics Subject Classification
- 49K20 49M25 49M29
- Optimal control, state constraints, boundary control, regularization, virtual control, numerical approximation, finite elements
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  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 problems.