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. The
contributions were written by Carla Manni and Hendrik Speelers Vibeke Skytt and Tor Dokken
Lourenco Beirao da Veiga Annalisa Buffa Giancarlo Sangalli and Rafael Vazquez and finally by
John Evans and Thomas J.R. Hughes.
