Local power of approximation in hierarchical spline spaces on weakly admissible meshes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913051348828160 |
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| author | Lezcano, Gustavo A. Fernandez Garau, Eduardo M. Ivaniszyn, Bárbara |
| author_facet | Lezcano, Gustavo A. Fernandez Garau, Eduardo M. Ivaniszyn, Bárbara |
| contents | We study local approximation properties in hierarchical spline spaces through a twofold approach. First, we design and analyze a robust adaptive refinement algorithm to construct locally graded meshes. Second, we establish rigorous stability and approximation results using computationally efficient quasi-interpolation operators. The primary contribution is the analysis of weakly admissible hierarchical meshes. Our framework relies on strictly nested cell sets that locally reproduce the full tensor-product spline space at each level. Theoretical and numerical results demonstrate that this intuitive approach is mathematically elegant and outperforms existing adaptive refinement strategies in various practical scenarios. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_19555 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local power of approximation in hierarchical spline spaces on weakly admissible meshes Lezcano, Gustavo A. Fernandez Garau, Eduardo M. Ivaniszyn, Bárbara Numerical Analysis We study local approximation properties in hierarchical spline spaces through a twofold approach. First, we design and analyze a robust adaptive refinement algorithm to construct locally graded meshes. Second, we establish rigorous stability and approximation results using computationally efficient quasi-interpolation operators. The primary contribution is the analysis of weakly admissible hierarchical meshes. Our framework relies on strictly nested cell sets that locally reproduce the full tensor-product spline space at each level. Theoretical and numerical results demonstrate that this intuitive approach is mathematically elegant and outperforms existing adaptive refinement strategies in various practical scenarios. |
| title | Local power of approximation in hierarchical spline spaces on weakly admissible meshes |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.19555 |