Complexity of hierarchical refinement for a class of admissible mesh configurations

Abstract

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 [6]. 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 finite element context, [3,24].

References in corpus (3)

• Axioms of Adaptivity
• Hierarchical analysis-suitable T-splines: Formulation, Bézier extraction, and application as an adaptive basis for isogeometric analysis
• Analysis-suitable adaptive T-mesh refinement with linear complexity

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• Rate optimality of adaptive finite element methods with respect to the overall computational costs
• Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines
• A hierarchical approach to the a posteriori error estimation of isogeometric Kirchhoff plates and Kirchhoff-Love shells
• Optimal convergence rates for goal-oriented FEM with quadratic goal functional
• The saturation assumption yields optimal convergence of two-level adaptive BEM