A priori error analysis of the proximal Galerkin method
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866918325639970816 |
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| author | Keith, Brendan Masri, Rami Zeinhofer, Marius |
| author_facet | Keith, Brendan Masri, Rami Zeinhofer, Marius |
| contents | The proximal Galerkin (PG) method is a finite element method for solving variational problems with inequality constraints. It has several advantages, including constraint-preserving approximations and mesh independence. This paper presents the first abstract a priori error analysis of PG methods, providing a general framework to establish convergence and error estimates. As applications of the framework, we demonstrate optimal convergence rates for both the obstacle and Signorini problems using various finite element subspaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A priori error analysis of the proximal Galerkin method Keith, Brendan Masri, Rami Zeinhofer, Marius Numerical Analysis 35J86, 35R35, 49J40, 65K15, 65N30 The proximal Galerkin (PG) method is a finite element method for solving variational problems with inequality constraints. It has several advantages, including constraint-preserving approximations and mesh independence. This paper presents the first abstract a priori error analysis of PG methods, providing a general framework to establish convergence and error estimates. As applications of the framework, we demonstrate optimal convergence rates for both the obstacle and Signorini problems using various finite element subspaces. |
| title | A priori error analysis of the proximal Galerkin method |
| topic | Numerical Analysis 35J86, 35R35, 49J40, 65K15, 65N30 |
| url | https://arxiv.org/abs/2507.13516 |