New refinable spaces and local approximation estimates for hierarchical splines
This work provides a theoretical foundation for more efficient local refinement in hierarchical splines, benefiting geometric modeling and isogeometric analysis.
The authors propose a subspace of hierarchical splines that retains essential properties while being more efficient for local refinement, using only parent-children relations for basis construction.
We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space (Vuong et al., 2011) which still satisfies the essential properties of the full space. The B-spline basis of such a subspace can be constructed using parent-children relations only, making it well adapted to local refinement algorithms.