Pressure-improved Scott-Vogelius type elements
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911790914338816 |
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| author | Bohne, Nis-Erik Gräßle, Benedikt Sauter, Stefan A. |
| author_facet | Bohne, Nis-Erik Gräßle, Benedikt Sauter, Stefan A. |
| contents | The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximation. However, it is well known that the convergence rates for the discrete pressure deteriorate in the presence of certain $critical$ $vertices$ in a triangulation of the domain. Modifications of the Scott-Vogelius element such as the recently introduced pressure-wired Stokes element also suffer from this effect. In this paper we introduce a simple modification strategy for these pressure spaces that preserves the inf-sup stability while the pressure converges at an optimal rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pressure-improved Scott-Vogelius type elements Bohne, Nis-Erik Gräßle, Benedikt Sauter, Stefan A. Numerical Analysis 65N30, 65N12, 76D07 The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximation. However, it is well known that the convergence rates for the discrete pressure deteriorate in the presence of certain $critical$ $vertices$ in a triangulation of the domain. Modifications of the Scott-Vogelius element such as the recently introduced pressure-wired Stokes element also suffer from this effect. In this paper we introduce a simple modification strategy for these pressure spaces that preserves the inf-sup stability while the pressure converges at an optimal rate. |
| title | Pressure-improved Scott-Vogelius type elements |
| topic | Numerical Analysis 65N30, 65N12, 76D07 |
| url | https://arxiv.org/abs/2403.04499 |