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We investigate discontinuous Galerkin methods for an elliptic optimal controlproblem with a general state equation and pointwise state constraints ongeneral polygonal domains. We show that discontinuous Galerkin methods forgeneral second-order elliptic boundary value problems can be used to solve theelliptic optimal control problems with pointwise state constraints. Weestablish concrete error estimates and numerical experiments are shown tosupport the theoretical results.

Discontinuous Galerkin Methods for an Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints