A divergence-free parametric finite element method for 3D Stokes equations on curved domains
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914207028477952 |
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| author | Li, Lingxiao Su, Haiyan Zhang, He Zheng, Weiying |
| author_facet | Li, Lingxiao Su, Haiyan Zhang, He Zheng, Weiying |
| contents | The Stokes equations play an important role in the incompressible flow simulation. In this paper, a novel divergence-free parametric mixed finite element method is proposed for solving three-dimensional Stokes equations on domains with piecewise smooth boundaries. The flow velocity and pressure are discretized with high-order parametric Brezzi-Douglas-Marini elements and volume elements, respectively, on curved tetrahedral meshes. Utilizing the interior-penalty discontinuous Galerkin (IPDG) technique, we prove the inf-sup condition for the mixed finite element pair, and high-order optimal error estimates in the energy norm, with the help of the extension and transformation of the true solution to computational domain. Moreover, the discrete velocity is exactly divergence-free, meaning that div uh = 0 holds in the curved computational domain. Numerical experiments are conducted to support the theoretical analyses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A divergence-free parametric finite element method for 3D Stokes equations on curved domains Li, Lingxiao Su, Haiyan Zhang, He Zheng, Weiying Numerical Analysis The Stokes equations play an important role in the incompressible flow simulation. In this paper, a novel divergence-free parametric mixed finite element method is proposed for solving three-dimensional Stokes equations on domains with piecewise smooth boundaries. The flow velocity and pressure are discretized with high-order parametric Brezzi-Douglas-Marini elements and volume elements, respectively, on curved tetrahedral meshes. Utilizing the interior-penalty discontinuous Galerkin (IPDG) technique, we prove the inf-sup condition for the mixed finite element pair, and high-order optimal error estimates in the energy norm, with the help of the extension and transformation of the true solution to computational domain. Moreover, the discrete velocity is exactly divergence-free, meaning that div uh = 0 holds in the curved computational domain. Numerical experiments are conducted to support the theoretical analyses. |
| title | A divergence-free parametric finite element method for 3D Stokes equations on curved domains |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.16216 |