TY - BOOK AU - Buffa,Annalisa AU - Sangalli,Giancarlo ED - International Mathematical Summer Centre TI - Isogeometric analysis: a new paradigm in the numerical approximation of PDEs T2 - Lecture notes in mathematics SN - 9783319423081 U1 - 511.6 23 PY - 2016/// CY - Switzerland : PB - Springer KW - Isogeometric analysis KW - Congresses KW - Geometric analysis N1 - Standard and non-standard CAGD tools for isogeometric analysis : a tutorial / Carla Manni and Hendrik Speleers -- Models for isogeometric analysis from CAD / Vibeke Skytt and Tor Dokken -- An introduction to the numerical analysis of isogeometric methods / L. Beirão da Veiga, A. Buffa, G. Sangalli, and R. Vázquez -- Isogeometric compatible discretizations for viscous incompressible flow / John A. Evans and Thomas J.R. Hughes N2 - 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. ER -