A NEW CONVERGENCE ANALYSIS OF FINITE ELEMENT METHODS FOR ELLIPTIC DISTRIBUTED OPTIMAL CONTROL PROBLEMS WITH POINTWISE STATE CONSTRAINTS

摘要

We consider finite element methods for elliptic distributed optimal control problems with pointwise state constraints on two and three dimensional convex polyhedral domains formulated as fourth order variational inequalities. We develop a new convergence analysis that is applicable to C-1 finite element methods, classical nonconforming finite element methods and discontinuous Galerkin methods.