Computational Optimization and Applications
Optimal Control for an Elliptic System with Polygonal State Constraints
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient State Constraints
SIAM Journal on Optimization
SIAM Journal on Control and Optimization
Stability of semilinear elliptic optimal control problems with pointwise state constraints
Computational Optimization and Applications
Error estimates for parabolic optimal control problems with control and state constraints
Computational Optimization and Applications
Calcolo: a quarterly on numerical analysis and theory of computation
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We consider an elliptic optimal control problem with control constraints and pointwise bounds on the gradient of the state. We present a tailored finite element approximation to this optimal control problem, where the cost functional is approximated by a sequence of functionals which are obtained by discretizing the state equation with the help of the lowest order Raviart–Thomas mixed finite element. Pointwise bounds on the gradient variable are enforced in the elements of the triangulation. Controls are not discretized. Error bounds for control and state are obtained in two and three space dimensions. A numerical example confirms our analytical findings.