Summation-by-parts operators for general function spaces: optimal nodes
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915958432464896 |
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| author | Hale, Nicholas Harley, Charis Nchupang, Prince Nordström, Jan |
| author_facet | Hale, Nicholas Harley, Charis Nchupang, Prince Nordström, Jan |
| contents | Gauss-Lobatto quadrature nodes and weights are optimal for closed summation-by-parts (SBP) formulations based on polynomial approximation spaces in the sense that for a prescribed function space they yield an SBP operator of minimal dimension. We show that the same principle extends to general (possibly non-polynomial) function spaces: an associated generalised Gauss-Lobatto quadrature provides the optimal nodes and weights for the SBP formulation. We present an algorithm for computing these quadrature rules, demonstrate their accuracy and efficiency across a range of function spaces, and illustrate their use in solving initial boundary value problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23306 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Summation-by-parts operators for general function spaces: optimal nodes Hale, Nicholas Harley, Charis Nchupang, Prince Nordström, Jan Numerical Analysis 65M12, 65M70, 65D32 Gauss-Lobatto quadrature nodes and weights are optimal for closed summation-by-parts (SBP) formulations based on polynomial approximation spaces in the sense that for a prescribed function space they yield an SBP operator of minimal dimension. We show that the same principle extends to general (possibly non-polynomial) function spaces: an associated generalised Gauss-Lobatto quadrature provides the optimal nodes and weights for the SBP formulation. We present an algorithm for computing these quadrature rules, demonstrate their accuracy and efficiency across a range of function spaces, and illustrate their use in solving initial boundary value problems. |
| title | Summation-by-parts operators for general function spaces: optimal nodes |
| topic | Numerical Analysis 65M12, 65M70, 65D32 |
| url | https://arxiv.org/abs/2604.23306 |