Error analysis for a Crouzeix-Raviart approximation of the obstacle problem
Numerical Analysis
2025-03-05 v3 Numerical Analysis
Abstract
In the present paper, we study a Crouzeix-Raviart approximation of the obstacle problem, which imposes the obstacle constraint in the midpoints (i.e., barycenters) of the elements of a triangulation. We establish a priori error estimates imposing natural regularity assumptions, which are optimal, and the reliability and efficiency of a primal-dual type a posteriori error estimator for general obstacles and involving data oscillation terms stemming only from the right-hand side. Numerical experiments are carried out to support the theoretical findings.
Cite
@article{arxiv.2302.01646,
title = {Error analysis for a Crouzeix-Raviart approximation of the obstacle problem},
author = {Sören Bartels and Alex Kaltenbach},
journal= {arXiv preprint arXiv:2302.01646},
year = {2025}
}
Comments
31 pages, 6 figures, 2 tables. arXiv admin note: text overlap with arXiv:2210.12116