A priori \(L^2\)-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints (Q681695)

The authors consider finite element discretization error estimates for convex elliptic optimal control problems with pointwise inequality constraints on the state. Some duality techniques presented in [\textit{D. Leykekhman} et al., Comput. Optim. Appl. 55, No. 3, 769--802 (2013; Zbl 1272.49049)] for finitely many equality state-constraints are extended to the case of finitely many inequality constraints. The main result is an a priori \(L^2\)-error estimate for the discretization error in the optimal states.