Complexity of hierarchical refinement for a class of admissible mesh configurations

An adaptive isogeometric method based on d-variate hierarchical spline constructions can be derived by considering a refine module that preserves a certain class of admissibility between two consecutive steps of the adaptive loop (Buffa and Giannelli, 2016). In this paper we provide a complexity estimate, i.e., an estimate on how the number of mesh elements grows with respect to the number of elements that are marked for refinement by the adaptive strategy. Our estimate is in the line of the similar ones proved in the context of adaptive finite element methods.