We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem and we propose multigrid methods to solve the discretized system. We prove that the $W$-cycle algorithm is uniformly convergent in the energy norm and is robust with respect to a regularization parameter on convex domains. Numerical results are shown for both $W$ -cycle and $V$-cycle algorithms.
Multigrid preconditioning for discontinuous Galerkin discretizations of an elliptic optimal control problem with a convection-dominated state equation
Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints
Robust multigrid methods for nearly incompressible elasticity using macro elements
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