Adaptive finite element methods for a fourth order obstacle problem and a state constrained optimal control problem

Abstract

This article discusses, a posteriori error analysis for HCT and Morley finite element methods for the fourth order obstacle problem (with simply supported boundary conditions) as well as for a distributed elliptic optimal control problem with pointwise state constraints. The distributed elliptic optimal control problem with pointwise state constraints is dealt by reducing it to a fourth order obstacle problem by eliminating the control variable. The reliability and efficiency of the underlying error estimator is discussed. Several numerical experiments are included illustrating that the error estimators work effectively in leading the adaptive mesh refinement and reducing the computational cost significantly.