A hierarchical construction of LR meshes in 2D

We describe a construction of LR-spaces whose bases are composed of locally linearly independent B-splines which also form a partition of unity. The construction conforms to given refinement requirements associated to subdomains. In contrast to the original LR-paper (Dokken et al., 2013) and similarly to the hierarchical B-spline framework (Forsey and Bartels, 1988) the construction of the mesh is based on a priori choice of a sequence of nested tensor B-spline spaces. The paper discusses bivariate LR splines with the non-nested support (N2S) property.Conditions on LR mesh refinement for preserving this property are presented.A hierarchical construction for LR meshes with the N2S property is proposed and analyzed.We prove the completeness of LR splines on the resulting hierarchical meshes.

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