IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs [electronic resource] : Cetraro, Italy 2012 / edited by Annalisa Buffa, Giancarlo Sangalli.

Preface -- Standard and Non‐Standard CAGD Tool for Isogeometric Analysis: a Tutorial -- Models for Isogeometric Analysis from CAD -- An Introduction to the Numerical Analysis of Isogeometric Methods -- Isogeometric Compatible Discretizations for Viscous Incompressible Flow.

Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric methods and their theoretical understanding. It contains a tutorial on splines and generalizations that are used in CAD parametrizations, and gives an overview of geometric modeling techniques that can be used within the isogeometric approach, with a focus on non-tensor product splines. Finally, it presents the mathematical properties of isogeometric spaces and spline spaces for vector field approximations, and treats in detail an application of fundamental importance: the isogeometric simulation of a viscous incompressible flow.