{A priori} error estimates for a state-constrained elliptic optimal control problem (Q2838578)

For elliptic control problems with state and control constraints in \(\mathbb{R}^3\) under homogeneous Dirichlet boundary conditions, an improved convergence rate is proven. The error estimate is at least of \({\mathcal O} (h^{\frac{3}{4}})\) when \(H^1\) regularity is provided for the optimal control. The control is discretized by piecewiese constant functions and the state by linear continuous finite elements. The derived convergence rate is verified numerically for a state-constrained optimal control problem on the unit ball \(B_1(0)\) in \(\mathbb{R}^3\).