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arXiv · 2604.19555

Local power of approximation in hierarchical spline spaces on weakly admissible meshes

Gustavo A. Fernandez Lezcano·Eduardo M. Garau·Bárbara Ivaniszyn
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Abstract

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.

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Gustavo A. Fernandez Lezcano, Eduardo M. Garau, Bárbara Ivaniszyn. 2026-04-21. Local power of approximation in hierarchical spline spaces on weakly admissible meshes. https://arxiv.org/abs/2604.19555

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