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

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. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This article discusses a posteriori error analysis for HCT and Morley finite element methods applied to the fourth order obstacle problem and the distributed elliptic optimal control problem with pointwise state constraints. The distributed elliptic optimal control problem is transformed into a fourth order obstacle problem by eliminating the control variable. The article examines the reliability and efficiency of the error estimator and presents numerical experiments that demonstrate its effectiveness in guiding adaptive mesh refinement and reducing computational cost.