H(curl)-based approximation of the Stokes problem with weakly enforced no-slip boundary conditions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912519685144576 |
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| author | Boon, Wietse M. Tonnon, Wouter Zampa, Enrico |
| author_facet | Boon, Wietse M. Tonnon, Wouter Zampa, Enrico |
| contents | In this work, we show how to impose no-slip boundary conditions for an H(curl)-based formulation for incompressible Stokes flow, which is used in structure-preserving discretizations of Navier-Stokes and magnetohydrodynamics equations. At first glance, it seems straightforward to apply no-slip boundary conditions: the tangential part is an essential boundary condition on H(curl) and the normal component can be naturally enforced through integration-by-parts of the divergence term. However, we show that this can lead to an ill-posed discretization and propose a Nitsche-based finite element method instead. We analyze the discrete system, establishing stability and deriving a priori error estimates. Numerical experiments validate our analysis and demonstrate optimal convergence rates for the velocity field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | H(curl)-based approximation of the Stokes problem with weakly enforced no-slip boundary conditions Boon, Wietse M. Tonnon, Wouter Zampa, Enrico Numerical Analysis 65N12, 65N30, 76D07 In this work, we show how to impose no-slip boundary conditions for an H(curl)-based formulation for incompressible Stokes flow, which is used in structure-preserving discretizations of Navier-Stokes and magnetohydrodynamics equations. At first glance, it seems straightforward to apply no-slip boundary conditions: the tangential part is an essential boundary condition on H(curl) and the normal component can be naturally enforced through integration-by-parts of the divergence term. However, we show that this can lead to an ill-posed discretization and propose a Nitsche-based finite element method instead. We analyze the discrete system, establishing stability and deriving a priori error estimates. Numerical experiments validate our analysis and demonstrate optimal convergence rates for the velocity field. |
| title | H(curl)-based approximation of the Stokes problem with weakly enforced no-slip boundary conditions |
| topic | Numerical Analysis 65N12, 65N30, 76D07 |
| url | https://arxiv.org/abs/2508.02861 |