Title: Mathematical Foundations of Finite Elements and Iterative Solvers (Computational Science and Engineering)
Publisher: SIAM - Society for Industrial and Applied Mathematics
Publication Date: 2022
Language: English
ISBN 10: 1611977088
ISBN 13: 9781611977080
Binding: Soft cover
Condition: New

About this title

Synopsis

This textbook describes the mathematical principles of the finite element method, a technique that turns a (linear) partial differential equation into a discrete linear system, often amenable to fast linear algebra. Reflecting the author’s decade of experience in the field, Mathematical Foundations of Finite Elements and Iterative Solvers examines the crucial interplay between analysis, discretization, and computations in modern numerical analysis; furthermore, it recounts historical developments leading to current state-of-the-art techniques. While self-contained, this textbook provides a clear and in-depth discussion of several topics, including elliptic problems, continuous Galerkin methods, iterative solvers, advection-diffusion problems, and saddle point problems. Accessible to readers with a beginning background in functional analysis and linear algebra, this text can be used in graduate-level courses on advanced numerical analysis, data science, numerical optimization, and approximation theory. Professionals in numerical analysis and finite element methods will also find the book of interest.

About the Author

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, �cole Polytechnique F�d�rale de Lausanne (EPFL), and RWTH Aachen. His research interests include hp-finite elements, fast algorithms for integral equations, and numerical linear algebra.

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