Mathematical Foundations of Adaptive Isogeometric Analysis
Annalisa Buffa, Gregor Gantner, Carlotta Giannelli, Dirk Praetorius, Rafael Vázquez
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 and the boundary element method in the frame of isogeometric analysis.
Topics & Concepts
Isogeometric analysisComputer scienceApplied mathematicsCalculus (dental)MathematicsMathematical optimizationFinite element methodEngineeringStructural engineeringMedicineDentistryAdvanced Numerical Analysis TechniquesIterative Methods for Nonlinear EquationsAdvanced Theoretical and Applied Studies in Material Sciences and Geometry