A Discontinuous Galerkin Method for Optimal Control of the Obstacle Problem
Numerical Analysis
2023-12-21 v1 Numerical Analysis
Optimization and Control
Abstract
This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty discontinuous Galerkin method. The main proofs are based on the improved -error estimates for the obstacle problem, the discrete maximum principle, and a well-known quadratic growth property. The standard (restrictive) assumptions on mesh are not assumed here.
Cite
@article{arxiv.2312.12582,
title = {A Discontinuous Galerkin Method for Optimal Control of the Obstacle Problem},
author = {Harbir Antil and Rohit Khandelwal and Umarkhon Rakhimov},
journal= {arXiv preprint arXiv:2312.12582},
year = {2023}
}