A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908752017358848 |
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| author | Garcke, Harald Nürnberg, Robert |
| author_facet | Garcke, Harald Nürnberg, Robert |
| contents | In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell \geq 2$. In the semidiscrete continuous-in-time setting we are able to prove a stability estimate that mimics a corresponding result for the continuous problem. Some numerical results, including a convergence experiment, demonstrate the practicality and accuracy of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface Garcke, Harald Nürnberg, Robert Numerical Analysis In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell \geq 2$. In the semidiscrete continuous-in-time setting we are able to prove a stability estimate that mimics a corresponding result for the continuous problem. Some numerical results, including a convergence experiment, demonstrate the practicality and accuracy of the proposed method. |
| title | A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.19198 |