Mathematical foundations of adaptive isogeometric analysis

Abstract

This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method (FEM) and the boundary element method (BEM) in the frame of isogeometric analysis (IGA).

References in corpus (3)

• Isogeometric boundary element method for acoustic scattering by a submarine
• BPX preconditioners for isogeometric analysis using analysis-suitable T-splines
• Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations

Cited by in corpus (7)

• Weighted quadrature for hierarchical B-splines
• Goal-Adaptive Meshing of Isogeometric Kirchhoff-Love Shells
• Isogeometric analysis of the Laplace eigenvalue problem on circular sectors: Regularity properties, graded meshes & variational crimes
• A short perspective on a posteriori error control and adaptive discretizations
• A Low-Frequency-Stable Higher-Order Isogeometric Discretization of the Augmented Electric Field Integral Equation
• Inexpensive polynomial-degree-robust equilibrated flux a posteriori estimates for isogeometric analysis
• Exact Integration for singular Zienkiewicz and Guzman-Neilan Finite Elements with Implementation