Mathematical Foundations of Finite Elements and Iterative Solvers

Paolo Gatto is senior lecturer at the Institute of Analysis and Scientific Computing at Vienna University of Technology. He has held postdoctoral positions at Brown University, Ecole Polytechnique Federale de Lausanne (EPFL), and RWTH Aachen. His research interests include hp-finite elements, fast algorithms for integral equations, and numerical linear algebra.

This book combines an updated look, at an advanced level, of the mathematical theory of the finite element method (including some important recent developments), and a presentation of many of the standard iterative methods for the numerical solution of the linear system of equations that results from finite element discretization, including saddle point problems arising from mixed finite element approximation. For the reader with some prior background in the subject, this text clarifies the importance of the essential ideas and provides a deeper understanding of how the basic concepts fit together."- Richard S. Falk, Rutgers University "Students of applied mathematics, engineering, and science will welcome this insightful and carefully crafted introduction to the mathematics of finite elements and to algorithms for iterative solvers. Concise, descriptive, and entertaining, the text covers all of the key mathematical ideas and concepts dealing with finite element approximations of problems in mechanics and physics governed by partial differential equations while interweaving basic concepts on Sobolev spaces and basic theorems of functional analysis presented in an effective tutorial style."- J. Tinsley Oden, The University of Texas at Austin