On The Weak Consistency of Finite Volumes Schemes for Conservation Laws on General Meshes
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866912037469159424 |
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| author | Gallouët, Thierry Herbin, R. Latché, J. -C |
| author_facet | Gallouët, Thierry Herbin, R. Latché, J. -C |
| contents | The aim of this paper is to develop some tools in order to obtain the weak consistency of (in other words, analogues of the Lax-Wendroff theorem for) finite volume schemes for balance laws in the multi-dimensional case and under minimal regularity assumptions for the mesh. As in the seminal Lax-Wendroff paper, our approach relies on a discrete integration by parts of the weak formulation of the scheme. This makes a discrete gradient of the test function appear, and the central argument for the scheme consistency is to remark that this discrete gradient is convergent in L $\infty$ weak . |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1906_02973 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On The Weak Consistency of Finite Volumes Schemes for Conservation Laws on General Meshes Gallouët, Thierry Herbin, R. Latché, J. -C Numerical Analysis The aim of this paper is to develop some tools in order to obtain the weak consistency of (in other words, analogues of the Lax-Wendroff theorem for) finite volume schemes for balance laws in the multi-dimensional case and under minimal regularity assumptions for the mesh. As in the seminal Lax-Wendroff paper, our approach relies on a discrete integration by parts of the weak formulation of the scheme. This makes a discrete gradient of the test function appear, and the central argument for the scheme consistency is to remark that this discrete gradient is convergent in L $\infty$ weak . |
| title | On The Weak Consistency of Finite Volumes Schemes for Conservation Laws on General Meshes |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1906.02973 |