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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.doi:10.1016/j.cma.2020.113230 fatcat:hjsajvksqzfb5ebpzjuwcczcye