Effective grading refinement for locally linearly independent LR B-splines

TL;DR

This paper introduces a novel refinement strategy for locally refined B-splines that maintains local linear independence, shape regularity, and quasi-uniformity, ensuring the basis spans the full spline space on refined meshes.

Contribution

The paper proposes a new refinement method for B-splines that guarantees local linear independence and full space coverage on locally refined meshes.

Findings

Ensures local linear independence of basis functions.

Maintains shape regularity and quasi-uniformity.

Guarantees the basis spans the entire spline space.

Abstract

We present a new refinement strategy for locally refined B-splines which ensures the local linear independence of the basis functions. The strategy also guarantees the spanning of the full spline space on the underlying locally refined mesh. The resulting mesh has nice grading properties which grant the preservation of shape regularity and local quasi uniformity of the elements in the refining process.