Convergent finite elements on arbitrary meshes, the WG method
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866929439541035008 |
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| author | Zhang, Ran Zhang, Shangyou |
| author_facet | Zhang, Ran Zhang, Shangyou |
| contents | On meshes with the maximum angle condition violated, the
standard conforming, nonconforming, and discontinuous Galerkin finite elements
do not converge to the true solution when the mesh size goes to zero.
It is shown that one type of weak Galerkin finite element method converges
on triangular and tetrahedral meshes violating the maximum angle condition,
i.e., on arbitrary meshes.
Numerical tests confirm the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergent finite elements on arbitrary meshes, the WG method Zhang, Ran Zhang, Shangyou Numerical Analysis On meshes with the maximum angle condition violated, the standard conforming, nonconforming, and discontinuous Galerkin finite elements do not converge to the true solution when the mesh size goes to zero. It is shown that one type of weak Galerkin finite element method converges on triangular and tetrahedral meshes violating the maximum angle condition, i.e., on arbitrary meshes. Numerical tests confirm the theory. |
| title | Convergent finite elements on arbitrary meshes, the WG method |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2407.19382 |