Pressure-robust and conforming discretization of the Stokes equations on anisotropic meshes
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911761008951296 |
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| author | Kempf, Volker |
| author_facet | Kempf, Volker |
| contents | Pressure-robust discretizations for incompressible flows have been in the focus of research for the past years. Many publications construct exactly divergence-free methods or use a reconstruction approach [13] for existing methods like the Crouzeix--Raviart element in order to achieve pressure-robustness. To the best of our knowledge, except for our recent publications [3,4], all those articles impose a condition on the shape-regularity of the mesh, and the two mentioned papers that allow for anisotropic elements use a non-conforming velocity approximation. Based on the classical Bernardi--Raugel element we provide a conforming pressure-robust discretization using the reconstruction approach on anisotropic meshes. Numerical examples support the theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_02756 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pressure-robust and conforming discretization of the Stokes equations on anisotropic meshes Kempf, Volker Numerical Analysis Pressure-robust discretizations for incompressible flows have been in the focus of research for the past years. Many publications construct exactly divergence-free methods or use a reconstruction approach [13] for existing methods like the Crouzeix--Raviart element in order to achieve pressure-robustness. To the best of our knowledge, except for our recent publications [3,4], all those articles impose a condition on the shape-regularity of the mesh, and the two mentioned papers that allow for anisotropic elements use a non-conforming velocity approximation. Based on the classical Bernardi--Raugel element we provide a conforming pressure-robust discretization using the reconstruction approach on anisotropic meshes. Numerical examples support the theory. |
| title | Pressure-robust and conforming discretization of the Stokes equations on anisotropic meshes |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2210.02756 |