Overview
- Structured to allow for concise development of ideas in a classroom setting
- Includes chapter-level exercises with solutions available online
- Provides proofs and examples throughout each chapter
- Aimed at a graduate study level with applications to engineering, researchers, and graduate-flipped classes
Part of the book series: Texts in Applied Mathematics (TAM, volume 72)
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Table of contents (23 chapters)
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Front Matter
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Elements of functional analysis
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Front Matter
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Introduction to finite elements
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Front Matter
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Finite element interpolation
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Front Matter
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Keywords
About this book
This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy.
Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.Authors and Affiliations
About the authors
Jean-Luc Guermond is Professor of Mathematics at Texas A&M University where he also holds an Exxon Mobile Chair in Computational Science. His current research interests are in numerical analysis, applied mathematics, and scientific computing. He has co-authored two books and over 170 research papers in peer-reviewed journals.
Bibliographic Information
Book Title: Finite Elements I
Book Subtitle: Approximation and Interpolation
Authors: Alexandre Ern, Jean-Luc Guermond
Series Title: Texts in Applied Mathematics
DOI: https://doi.org/10.1007/978-3-030-56341-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-56340-0Published: 19 February 2021
Softcover ISBN: 978-3-030-56342-4Published: 20 February 2022
eBook ISBN: 978-3-030-56341-7Published: 18 February 2021
Series ISSN: 0939-2475
Series E-ISSN: 2196-9949
Edition Number: 1
Number of Pages: XII, 325
Number of Illustrations: 90 b/w illustrations