A high order, block finite difference, error inhibiting scheme for the transport equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916130669461504 |
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| author | Ditkowski, Adi Blanc, Anne Le Shu, Chi-Wang |
| author_facet | Ditkowski, Adi Blanc, Anne Le Shu, Chi-Wang |
| contents | We propose a block finite difference, error inhibiting scheme that is fourth-order accurate for short to moderate times and has a six-order convergence rate for long times. This scheme outperforms the standard fourth-order Finite Difference scheme. We also demonstrate that the proposed scheme is a particular type of nodal-based Discontinuous Galerkin method with $p=1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_11617 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A high order, block finite difference, error inhibiting scheme for the transport equation Ditkowski, Adi Blanc, Anne Le Shu, Chi-Wang Numerical Analysis 65M06, 65M12, 65M15, 65M60 G.1.8 We propose a block finite difference, error inhibiting scheme that is fourth-order accurate for short to moderate times and has a six-order convergence rate for long times. This scheme outperforms the standard fourth-order Finite Difference scheme. We also demonstrate that the proposed scheme is a particular type of nodal-based Discontinuous Galerkin method with $p=1$. |
| title | A high order, block finite difference, error inhibiting scheme for the transport equation |
| topic | Numerical Analysis 65M06, 65M12, 65M15, 65M60 G.1.8 |
| url | https://arxiv.org/abs/2402.11617 |