On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems
Numerical Analysis
2026-05-27 v1 Numerical Analysis
Abstract
We present new convergence estimates for the iterated penalty method applied to structure-preserving discretizations of linear generalized saddle point systems. The method may be viewed as an Uzawa iteration on an augmented Lagrangian formulation of the system. As a by-product, we obtain sharper stability estimates for penalized/perturbed saddle point problems. Three model finite element applications show agreement with the theory.
Keywords
Cite
@article{arxiv.2605.27069,
title = {On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems},
author = {Patrick E. Farrell and Michael Neilan and Charles Parker and L. Ridgway Scott},
journal= {arXiv preprint arXiv:2605.27069},
year = {2026}
}