Adaptive refinement with locally linearly independent LR B-splines: Theory and applications

Abstract

In this paper we describe an adaptive refinement strategy for LR B-splines. The presented strategy ensures, at each iteration, local linear independence of the obtained set of LR B-splines. This property is then exploited in two applications: the construction of efficient quasi-interpolation schemes and the numerical solution of elliptic problems using the isogeometric Galerkin method.

arXiv comment23 pages, 14 figures

References in corpus (1)

• Linear dependence of bivariate Minimal Support and Locally Refined B-splines over LR-meshes

Cited by in corpus (5)

• Mathematical foundations of adaptive isogeometric analysis
• Weighted Quasi Interpolant Spline Approximations: Properties and Applications
• Quasi-interpolation projectors for Subdivision Surfaces
• Basis construction for polynomial spline spaces over arbitrary T-meshes
• Immersed Boundary-Conformal Isogeometric Method for Linear Elliptic Problems