Pressure-Robust Fortin-Soulie Elements of the Stokes Equation on Curved Domains
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910129176182784 |
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| author | Chen, Wei Liu, Zhen |
| author_facet | Chen, Wei Liu, Zhen |
| contents | This paper presents a pressure-robust and element-wise divergence-free nonconforming finite element method for the Stokes problem on curved domains. The discrete element is constructed by mapping the Fortin-Soulie element from a reference triangle using an isoparametric mapping for the geometry and a Piola transform for the function space. The inf-sup condition and the error estimate with optimal convergence rate are proved. Pressure-robustness is obtained by replacing the discrete velocity test functions with the first-order Raviart-Thomas functions. Numerical examples are provided to validate the theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_12769 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pressure-Robust Fortin-Soulie Elements of the Stokes Equation on Curved Domains Chen, Wei Liu, Zhen Numerical Analysis 65N30, %Stability and convergence of numerical methods 65N12, %Error bounds 65N30, 65N12, 76M10 This paper presents a pressure-robust and element-wise divergence-free nonconforming finite element method for the Stokes problem on curved domains. The discrete element is constructed by mapping the Fortin-Soulie element from a reference triangle using an isoparametric mapping for the geometry and a Piola transform for the function space. The inf-sup condition and the error estimate with optimal convergence rate are proved. Pressure-robustness is obtained by replacing the discrete velocity test functions with the first-order Raviart-Thomas functions. Numerical examples are provided to validate the theoretical results. |
| title | Pressure-Robust Fortin-Soulie Elements of the Stokes Equation on Curved Domains |
| topic | Numerical Analysis 65N30, %Stability and convergence of numerical methods 65N12, %Error bounds 65N30, 65N12, 76M10 |
| url | https://arxiv.org/abs/2604.12769 |