Multigrid methods for an elliptic optimal control problem with pointwise state constraints

Abstract

We design multigrid methods for an elliptic distributed optimal control problem with pointwise state constraints. They are based on the P1 finite element method from Brenner et al. (2021), where the optimal control problem was reformulated as a variational inequality for the state variable. The performance of the multigrid methods is illustrated by numerical experiments.

Keywords

• Elliptic distributed optimal control problems
• Pointwise state constraints
• Multigrid methods
• P1 finite element method
• Primal–dual active set algorithm