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 Bsplines. This property is then exploited in two applications: the construction of efficient quasiinterpolation schemes and the numerical solution of elliptic problems using the isogeometric Galerkin method.