On the stability of finite-volume schemes on non-uniform meshes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929478576373760 |
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| author | Bakhvalov, Pavel Surnachev, Mikhail |
| author_facet | Bakhvalov, Pavel Surnachev, Mikhail |
| contents | In this paper, we study the L2 stability of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider the case when a small periodic perturbation is applied to a uniform mesh. For this case, we establish a sufficient stability condition. This allows to prove the (p+1)-th order convergence of finite-volume schemes based on p-th order polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the stability of finite-volume schemes on non-uniform meshes Bakhvalov, Pavel Surnachev, Mikhail Numerical Analysis 65M12 In this paper, we study the L2 stability of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider the case when a small periodic perturbation is applied to a uniform mesh. For this case, we establish a sufficient stability condition. This allows to prove the (p+1)-th order convergence of finite-volume schemes based on p-th order polynomials. |
| title | On the stability of finite-volume schemes on non-uniform meshes |
| topic | Numerical Analysis 65M12 |
| url | https://arxiv.org/abs/2408.16511 |