Error estimates of $hp$-finite element method for elliptic optimal control problems with robin boundary
Numerical Analysis
2026-01-29 v1 Numerical Analysis
Optimization and Control
Abstract
A priori and a posteriori error analysis of finite element method for elliptic control problem with Robin boundary condition and boundary observation are presented. are presented. Through the Cl\'ement-type approach and the construction of an auxiliary system, we derived a priori error estimates for the elliptic optimal control problem. Residual-based a posteriori error estimates are derived based on the well-known Scott-Zhang-type quasi-interpolation and coupled state-control approximations, thus establishing an a posteriori error estimator for the finite element method. The numerical example demonstrates the accuracy of error estimation for the elliptic optimal control problems with Robin boundary.
Cite
@article{arxiv.2601.20145,
title = {Error estimates of $hp$-finite element method for elliptic optimal control problems with robin boundary},
author = {Xingyuan Lin and Xiuxiu Lin and Xuesong Chen},
journal= {arXiv preprint arXiv:2601.20145},
year = {2026}
}