New refinable spaces and local approximation estimates for hierarchical splines

TL;DR

This paper introduces a new subspace of hierarchical spline spaces with enhanced local approximation properties, constructed via multiscale quasi-interpolation, facilitating efficient local refinement in isogeometric analysis.

Contribution

It proposes a novel subspace of hierarchical splines with improved local approximation estimates, constructed using parent-children relations for better local refinement.

Findings

The new subspace retains essential properties of the full hierarchical spline space.

The basis construction is simplified using parent-children relations.

The approach enhances local approximation capabilities in hierarchical spline spaces.

Abstract

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.