Stokes problem with slip boundary conditions using stabilized finite elements combined with Nitsche
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929313220132864 |
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| author | Araya, Rodolfo Caiazzo, Alfonso Chouly, Franz |
| author_facet | Araya, Rodolfo Caiazzo, Alfonso Chouly, Franz |
| contents | We discuss how slip conditions for the Stokes equation can be handled using Nitsche method, for a stabilized finite element discretization. Emphasis is made on the interplay between stabilization and Nitsche terms. Well-posedness of the discrete problem and optimal convergence rates, in natural norm for the velocity and the pressure, are established, and illustrated with various numerical experiments. The proposed method fits naturally in the context of a finite element implementation while being accurate, and allows an increased flexibility in the choice of the finite element pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stokes problem with slip boundary conditions using stabilized finite elements combined with Nitsche Araya, Rodolfo Caiazzo, Alfonso Chouly, Franz Numerical Analysis 65M60 65M60, 76M10 G.1.8 We discuss how slip conditions for the Stokes equation can be handled using Nitsche method, for a stabilized finite element discretization. Emphasis is made on the interplay between stabilization and Nitsche terms. Well-posedness of the discrete problem and optimal convergence rates, in natural norm for the velocity and the pressure, are established, and illustrated with various numerical experiments. The proposed method fits naturally in the context of a finite element implementation while being accurate, and allows an increased flexibility in the choice of the finite element pairs. |
| title | Stokes problem with slip boundary conditions using stabilized finite elements combined with Nitsche |
| topic | Numerical Analysis 65M60 65M60, 76M10 G.1.8 |
| url | https://arxiv.org/abs/2404.08810 |