Auto-Stabilized Weak Galerkin Finite Element Methods for Stokes Equations on Non-Convex Polytopal Meshes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913636746788864 |
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| author | Wang, Chunmei Zhang, Shangyou |
| author_facet | Wang, Chunmei Zhang, Shangyou |
| contents | This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for solving Stokes equations without relying on traditional stabilizers. The proposed WG method accommodates both convex and non-convex polytopal elements in finite element partitions, leveraging bubble functions as a key analytical tool. The simplified WG method is symmetric and positive definite, and optimal-order error estimates are derived for WG approximations in both the discrete $H^1$ norm and the $L^2$ norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Auto-Stabilized Weak Galerkin Finite Element Methods for Stokes Equations on Non-Convex Polytopal Meshes Wang, Chunmei Zhang, Shangyou Numerical Analysis 65N30, 65N15, 65N12, 65N20 This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for solving Stokes equations without relying on traditional stabilizers. The proposed WG method accommodates both convex and non-convex polytopal elements in finite element partitions, leveraging bubble functions as a key analytical tool. The simplified WG method is symmetric and positive definite, and optimal-order error estimates are derived for WG approximations in both the discrete $H^1$ norm and the $L^2$ norm. |
| title | Auto-Stabilized Weak Galerkin Finite Element Methods for Stokes Equations on Non-Convex Polytopal Meshes |
| topic | Numerical Analysis 65N30, 65N15, 65N12, 65N20 |
| url | https://arxiv.org/abs/2501.02590 |