Prof. Dr. Susanne C. Brenner | Louisiana State University | United States
We consider finite element methods for a model linear-quadratic elliptic distributed optimal control problem with pointwise state constraints. For convex or smooth domains, this problem can be reformulated as a fourth order variational inequality that can be solved by many finite element methods originally designed for fourth order elliptic boundary value problems. We will present a general convergence analysis that can be applied to conforming, nonconforming and discontinuous Galerkin methods. We will also discuss the extension of this analysis to a P1 finite element method for the optimal control problem on nonconvex polyhedral domains.