Explicit T -coercivity for the Stokes problem: a coercive finite element discretization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913553482514432 |
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| author | Ciarlet Jr, Patrick Jamelot, Erell |
| author_facet | Ciarlet Jr, Patrick Jamelot, Erell |
| contents | Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients (2013)], we propose a new variational formulation of the Stokes problem which does not involve nonlocal operators. With this new formulation, unstable finite element pairs are stabilized. In addition, the numerical scheme is easy to implement, and a better approximation of the velocity and the pressure is observed numerically when the viscosity is small. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_14444 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit T -coercivity for the Stokes problem: a coercive finite element discretization Ciarlet Jr, Patrick Jamelot, Erell Numerical Analysis 65N30 35J57 76D07 Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients (2013)], we propose a new variational formulation of the Stokes problem which does not involve nonlocal operators. With this new formulation, unstable finite element pairs are stabilized. In addition, the numerical scheme is easy to implement, and a better approximation of the velocity and the pressure is observed numerically when the viscosity is small. |
| title | Explicit T -coercivity for the Stokes problem: a coercive finite element discretization |
| topic | Numerical Analysis 65N30 35J57 76D07 |
| url | https://arxiv.org/abs/2410.14444 |