Hybrid weakly over-penalised symmetric interior penalty method on anisotropic meshes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929631441977344 |
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| author | Ishizaka, Hiroki |
| author_facet | Ishizaka, Hiroki |
| contents | In this study, we investigate a hybrid-type anisotropic weakly over-penalised symmetric interior penalty method for the Poisson equation on convex domains. Compared with the well-known hybrid discontinuous Galerkin methods, our approach is simple and easy to implement. Our primary contributions are the proposal of a new scheme and the demonstration of a proof for the consistency term, which allows us to estimate the anisotropic consistency error. The key idea of the proof is to apply the relation between the Raviart--Thomas finite element space and a discontinuous space. In numerical experiments, we compare the calculation results for standard and anisotropic mesh partitions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_15288 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid weakly over-penalised symmetric interior penalty method on anisotropic meshes Ishizaka, Hiroki Numerical Analysis In this study, we investigate a hybrid-type anisotropic weakly over-penalised symmetric interior penalty method for the Poisson equation on convex domains. Compared with the well-known hybrid discontinuous Galerkin methods, our approach is simple and easy to implement. Our primary contributions are the proposal of a new scheme and the demonstration of a proof for the consistency term, which allows us to estimate the anisotropic consistency error. The key idea of the proof is to apply the relation between the Raviart--Thomas finite element space and a discontinuous space. In numerical experiments, we compare the calculation results for standard and anisotropic mesh partitions. |
| title | Hybrid weakly over-penalised symmetric interior penalty method on anisotropic meshes |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.15288 |