Mathematical foundations of adaptive isogeometric analysis
Annalisa Buffa, Gregor Gantner, Carlotta Giannelli, Dirk Praetorius,, Rafael V\'azquez
TL;DR
This paper reviews the mathematical foundations and recent developments in adaptive isogeometric analysis, focusing on spline technologies, convergence, and optimality of adaptive algorithms for FEM and BEM within IGA.
Contribution
It provides a comprehensive overview of the mathematical theory, spline technologies, and convergence results for adaptive IGA, highlighting recent advances.
Findings
Overview of spline technologies for local resolution
Formulation of convergence and quasi-optimality results
Discussion of adaptive algorithms for FEM and BEM in IGA
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).
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Iterative Methods for Nonlinear Equations · Polynomial and algebraic computation