DOI: 10.1515/cmam-2023-0083 ISSN: 1609-4840
Convergence of Adaptive CrouzeixâRaviart and Morley FEM for Distributed Optimal Control Problems
Asha K. Dond, Neela Nataraj, Subham Nayak Abstract
This article discusses the quasi-optimality of adaptive nonconforming finite element methods for distributed optimal control problems governed by đ-harmonic operators for
m
=
1
,
2
m=1,2
.
A variational discretization approach is employed and the state and adjoint variables are discretized using nonconforming finite elements.
Error equivalence results at the continuous and discrete levels lead to a priori and a posteriori error estimates for the optimal control problem.
The general axiomatic framework that includes stability, reduction, discrete reliability, and quasi-orthogonality establishes the quasi-optimality.
Numerical results demonstrate the theoretically predicted orders of convergence and the efficiency of the adaptive estimator.