Mathematical Foundations of Adaptive Isogeometric Analysis

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-...

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Published inArchives of computational methods in engineering Vol. 29; no. 7; pp. 4479 - 4555
Main Authors Buffa, Annalisa, Gantner, Gregor, Giannelli, Carlotta, Praetorius, Dirk, Vázquez, Rafael
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 2022
Springer Nature B.V
Subjects
Adaptive algorithms
Boundary element method
Engineering
Finite element method
Mathematical analysis
Mathematical and Computational Engineering
Review
Review Article
State-of-the-art reviews
65N12
65N38
65N50
65Y20
41A15
65D07
65N30
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Summary: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 and the boundary element method in the frame of isogeometric analysis.
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ISSN:1134-3060
1886-1784
1886-1784
DOI:10.1007/s11831-022-09752-5