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arXiv · 2605.27069

On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems

Patrick E. Farrell·Michael Neilan·Charles Parker·L. Ridgway Scott
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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.

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Patrick E. Farrell, Michael Neilan, Charles Parker, L. Ridgway Scott. 2026-05-26. On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems. https://arxiv.org/abs/2605.27069

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