Auto-Stabilized Weak Galerkin Finite Element Methods on Polytopal Meshes without Convexity Constraints
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914920583397376 |
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| author | Wang, Chunmei |
| author_facet | Wang, Chunmei |
| contents | This paper introduces an auto-stabilized weak Galerkin (WG) finite element method with a built-in stabilizer for Poisson equations. By utilizing bubble functions as a key analytical tool, our method extends to both convex and non-convex elements in finite element partitions, marking a significant advancement over existing stabilizer-free WG methods. It overcomes the restrictive conditions of previous approaches and is applicable in any dimension $d$, offering substantial advantages. The proposed method maintains a simple, symmetric, and positive definite structure. These benefits are evidenced by optimal order error estimates in both discrete $H^1$ and $L^2$ norms, highlighting the effectiveness and accuracy of our WG method for practical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11927 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Auto-Stabilized Weak Galerkin Finite Element Methods on Polytopal Meshes without Convexity Constraints Wang, Chunmei Numerical Analysis 65N30, 65N15, 65N12, 65N20 This paper introduces an auto-stabilized weak Galerkin (WG) finite element method with a built-in stabilizer for Poisson equations. By utilizing bubble functions as a key analytical tool, our method extends to both convex and non-convex elements in finite element partitions, marking a significant advancement over existing stabilizer-free WG methods. It overcomes the restrictive conditions of previous approaches and is applicable in any dimension $d$, offering substantial advantages. The proposed method maintains a simple, symmetric, and positive definite structure. These benefits are evidenced by optimal order error estimates in both discrete $H^1$ and $L^2$ norms, highlighting the effectiveness and accuracy of our WG method for practical applications. |
| title | Auto-Stabilized Weak Galerkin Finite Element Methods on Polytopal Meshes without Convexity Constraints |
| topic | Numerical Analysis 65N30, 65N15, 65N12, 65N20 |
| url | https://arxiv.org/abs/2408.11927 |