Convergence rate of the spectral difference method on regular triangular meshes
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910411948818432 |
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| author | Bakhvalov, Pavel |
| author_facet | Bakhvalov, Pavel |
| contents | We consider the spectral difference method based on the p-th order Raviart~-- Thomas space (p=1,2,3) on regular triangular meshes for the scalar transport equation. The solution converges with the order p if the transport velocity is parallel to a family of mesh edges and with the order p+1 otherwise. We prove this fact for p=1 and show it for p=1,2,3 in numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10391 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence rate of the spectral difference method on regular triangular meshes Bakhvalov, Pavel Numerical Analysis 65M12 G.1.8 We consider the spectral difference method based on the p-th order Raviart~-- Thomas space (p=1,2,3) on regular triangular meshes for the scalar transport equation. The solution converges with the order p if the transport velocity is parallel to a family of mesh edges and with the order p+1 otherwise. We prove this fact for p=1 and show it for p=1,2,3 in numerical experiments. |
| title | Convergence rate of the spectral difference method on regular triangular meshes |
| topic | Numerical Analysis 65M12 G.1.8 |
| url | https://arxiv.org/abs/2404.10391 |