Finite element approximation of the stationary Navier-Stokes problem with non-smooth data
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918325673525248 |
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| author | Armentano, María Gabriela Mendiluce, Mauricio |
| author_facet | Armentano, María Gabriela Mendiluce, Mauricio |
| contents | The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes system with a regularized boundary solution. Based on the existence of the very weak solution for the Navier-Stokes system with L2 boundary data, and a suitable decomposition of this solution, we obtain a priori error estimates between the approximation of the Navier-Stokes system with non-smooth data and the finite element solution of the associated regularized problem. These estimates allow us to conclude that our approach converges with optimal order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite element approximation of the stationary Navier-Stokes problem with non-smooth data Armentano, María Gabriela Mendiluce, Mauricio Numerical Analysis 65N15 65N30 The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes system with a regularized boundary solution. Based on the existence of the very weak solution for the Navier-Stokes system with L2 boundary data, and a suitable decomposition of this solution, we obtain a priori error estimates between the approximation of the Navier-Stokes system with non-smooth data and the finite element solution of the associated regularized problem. These estimates allow us to conclude that our approach converges with optimal order. |
| title | Finite element approximation of the stationary Navier-Stokes problem with non-smooth data |
| topic | Numerical Analysis 65N15 65N30 |
| url | https://arxiv.org/abs/2509.16461 |