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We investigate aP1P_{1}finite element method for an elliptic distributed optimal control problem with pointwise state constraints and a state equation that includes advective/convective and reactive terms. The convergence of this method can be established for general polygonal/polyhedral domains that are not necessarily convex. The discrete problem is a strictly convex quadratic program with box constraints that can be solved efficiently by a primal-dual active set algorithm.

A 𝑃 1 Finite Element Method for a Distributed Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints