Local power of approximation in hierarchical spline spaces on weakly admissible meshes
Provides a mathematically elegant and computationally efficient framework for adaptive mesh refinement in spline-based approximation, benefiting fields like isogeometric analysis and numerical simulation.
The paper introduces a robust adaptive refinement algorithm for hierarchical spline spaces on weakly admissible meshes, proving stability and approximation results that outperform existing strategies in practical scenarios.
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.