The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme. II
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910464341966848 |
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| author | Benoit, Antoine Coulombel, Jean-François |
| author_facet | Benoit, Antoine Coulombel, Jean-François |
| contents | We study the stability of a two-dimensional Lax-Wendroff scheme in a quarter-plane. Following our previous work, we aim here at adapting the energy method in order to study second order extrapolation boundary conditions. We first show on the one-dimensional problem why modifying the energy is a necessity in order to obtain stability estimates. We then study the two-dimensional case and propose a modified energy as well as second order extrapolation boundary and corner conditions in order to maintain second order accuracy and stability of the whole scheme, including near the corner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19844 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme. II Benoit, Antoine Coulombel, Jean-François Numerical Analysis We study the stability of a two-dimensional Lax-Wendroff scheme in a quarter-plane. Following our previous work, we aim here at adapting the energy method in order to study second order extrapolation boundary conditions. We first show on the one-dimensional problem why modifying the energy is a necessity in order to obtain stability estimates. We then study the two-dimensional case and propose a modified energy as well as second order extrapolation boundary and corner conditions in order to maintain second order accuracy and stability of the whole scheme, including near the corner. |
| title | The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme. II |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.19844 |