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

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. •A simple adaptive refinement for locally linearly independent LR B-splines is presented.•An efficient and effortless quasi-interpolation scheme with LR B-splines is described.•The new refinement is also adopted to perform isogeometric analysis with LR B-splines.