A Monolithic Discontinuous Galerkin Framework for Darcy Optimal Control with Radon-Measure Tracking and Pointwise Control Constraints

This paper studies an elliptic optimal control problem governed by Darcy's equation in heterogeneous porous media, with pointwise box constraints imposed on the control. The objective functional is formulated through a Radon measure, allowing the desired pressure state to be tracked simultaneously on observation sets of differing dimension — points, curves, and subdomains — within one formulation. The state and adjoint equations are discretized using a symmetric interior-penalty discontinuous Galerkin approach within a monolithic framework.