A non-separable progressive multivariate WENO-$2r$ point value
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910423327965184 |
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| author | Mulet, Pep Ruiz-Alvarez, Juan Shu, Chi-Wang Yáñez, Dionisio F. |
| author_facet | Mulet, Pep Ruiz-Alvarez, Juan Shu, Chi-Wang Yáñez, Dionisio F. |
| contents | The weighted essentially non-oscillatory {technique} using a stencil of $2r$ points (WENO-$2r$) is an interpolatory method that consists in obtaining a higher approximation order from the non-linear combination of interpolants of $r+1$ nodes. The result is an interpolant of order $2r$ at the smooth parts and order $r+1$ when an isolated discontinuity falls at any grid interval of the large stencil except at the central one. Recently, a new WENO method based on Aitken-Neville's algorithm has been designed for interpolation of equally spaced data at the mid-points and presents progressive order of accuracy close to discontinuities. This paper is devoted to constructing a general progressive WENO method for non-necessarily uniformly spaced data and several variables interpolating in any point of the central interval. Also, we provide explicit formulas for linear and non-linear weights and prove the order obtained. Finally, some numerical experiments are presented to check the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A non-separable progressive multivariate WENO-$2r$ point value Mulet, Pep Ruiz-Alvarez, Juan Shu, Chi-Wang Yáñez, Dionisio F. Numerical Analysis The weighted essentially non-oscillatory {technique} using a stencil of $2r$ points (WENO-$2r$) is an interpolatory method that consists in obtaining a higher approximation order from the non-linear combination of interpolants of $r+1$ nodes. The result is an interpolant of order $2r$ at the smooth parts and order $r+1$ when an isolated discontinuity falls at any grid interval of the large stencil except at the central one. Recently, a new WENO method based on Aitken-Neville's algorithm has been designed for interpolation of equally spaced data at the mid-points and presents progressive order of accuracy close to discontinuities. This paper is devoted to constructing a general progressive WENO method for non-necessarily uniformly spaced data and several variables interpolating in any point of the central interval. Also, we provide explicit formulas for linear and non-linear weights and prove the order obtained. Finally, some numerical experiments are presented to check the theoretical results. |
| title | A non-separable progressive multivariate WENO-$2r$ point value |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.16694 |