Numerical models for differential problems (Q2012678)

The second edition of this volume has been the subject of the review [\textit{A. Quarteroni}, Numerical models for differential problems. Translated from the 5th Italian edition by Silvia Quarteroni. 2nd ed. Milano: Springer (2014; Zbl 1285.65054)]. With respect to this new edition, the author added one chapter, now Chapter 11 ``Isogeometric analysis'' (IGA), considerably improved the chapter (now Chapter 20) ``Reduced basis methods'' and revised the whole text. The volume also contains a detailed preface to the second edition, references and an index. In the new chapter the author analyses the so-called NURBS (Non Rational Uniform B-splines)-based IGA in the framework of Galerkin scheme. He is mainly concerned with the isogeometric concept, its algebraic aspects, and a priori error estimates in the context of the homogeneous Dirichlet boundary value problem attached to the Poisson equation.