Discontinuous Finite Volume Element Methods for the Optimal Control of Brinkman Equations

We introduce and analyse a family of hybrid discretisations based on lowest order discontinuous finite volume elements for the approximation of optimal control problems constrained by the Brinkman equations. The classical optimise-then-discretise approach is employed to handle the control problem leading to a non-symmetric discrete formulation. An a priori error estimate is derived for the control variable in the L-2 - norm, and we exemplify the properties of the method with a numerical test in 3D.