On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917536502644736 |
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| author | Farrell, Patrick E. Neilan, Michael Parker, Charles Scott, L. Ridgway |
| author_facet | Farrell, Patrick E. Neilan, Michael Parker, Charles Scott, L. Ridgway |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27069 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems Farrell, Patrick E. Neilan, Michael Parker, Charles Scott, L. Ridgway Numerical Analysis 65N22, 65F10, 15A06 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. |
| title | On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems |
| topic | Numerical Analysis 65N22, 65F10, 15A06 |
| url | https://arxiv.org/abs/2605.27069 |