Stabilizer-free Weak Galerkin Methods for Quad-Curl Problems on polyhedral Meshes without Convexity Assumptions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916608727842816 |
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| author | Wang, Chunmei Zhang, Shangyou |
| author_facet | Wang, Chunmei Zhang, Shangyou |
| contents | This paper introduces an efficient stabilizer-free weak Galerkin (WG) finite element method for solving the three-dimensional quad-curl problem. Leveraging bubble functions as a key analytical tool, the method extends the applicability of stabilizer-free WG approaches to non-convex elements in finite element partitions-a notable advancement over existing methods, which are restricted to convex elements. The proposed method maintains a simple, symmetric, and positive definite formulation. It achieves optimal error estimates for the exact solution in a discrete norm, as well as an optimal-order $L^2$ error estimate for $k>2$ and a sub-optimal order for the lowest order case $k=2$. Numerical experiments are presented to validate the method's efficiency and accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stabilizer-free Weak Galerkin Methods for Quad-Curl Problems on polyhedral Meshes without Convexity Assumptions Wang, Chunmei Zhang, Shangyou Numerical Analysis Primary, 65N30, 65N15, 65N12, 74N20, Secondary, 35B45, 35J50, 35J35 This paper introduces an efficient stabilizer-free weak Galerkin (WG) finite element method for solving the three-dimensional quad-curl problem. Leveraging bubble functions as a key analytical tool, the method extends the applicability of stabilizer-free WG approaches to non-convex elements in finite element partitions-a notable advancement over existing methods, which are restricted to convex elements. The proposed method maintains a simple, symmetric, and positive definite formulation. It achieves optimal error estimates for the exact solution in a discrete norm, as well as an optimal-order $L^2$ error estimate for $k>2$ and a sub-optimal order for the lowest order case $k=2$. Numerical experiments are presented to validate the method's efficiency and accuracy. |
| title | Stabilizer-free Weak Galerkin Methods for Quad-Curl Problems on polyhedral Meshes without Convexity Assumptions |
| topic | Numerical Analysis Primary, 65N30, 65N15, 65N12, 74N20, Secondary, 35B45, 35J50, 35J35 |
| url | https://arxiv.org/abs/2502.07795 |