English

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}
}