Texts in Applied Mathematics

Finite Elements I

Approximation and Interpolation

Authors: Ern, Alexandre, Guermond, Jean-Luc

Free Preview
  • 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
see more benefits

Buy this book

eBook $59.99
price for USA in USD
  • Due: April 19, 2021
  • ISBN 978-3-030-56341-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
Hardcover $79.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: February 19, 2021
  • ISBN 978-3-030-56340-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
About this Textbook

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.

About the authors

Alexandre Ern is Senior Researcher at Ecole des Ponts and INRIA in Paris, and he is also Associate Professor of Numerical Analysis at Ecole Polytechnique, Paris. His research deals with the devising and analysis of finite element methods and a posteriori error estimates and adaptivity with applications to fluid and solid mechanics and porous media flows. Alexandre Ern has co-authored three books and over 150 papers in peer-reviewed journals. He has supervised about 20 PhD students and 10 post-doctoral fellows, and he has ongoing collaborations with several industrial partners. 
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.


Table of contents (23 chapters)

Table of contents (23 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • Due: April 19, 2021
  • ISBN 978-3-030-56341-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
Hardcover $79.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: February 19, 2021
  • ISBN 978-3-030-56340-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Finite Elements I
Book Subtitle
Approximation and Interpolation
Authors
Series Title
Texts in Applied Mathematics
Series Volume
72
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-56341-7
DOI
10.1007/978-3-030-56341-7
Hardcover ISBN
978-3-030-56340-0
Series ISSN
0939-2475
Edition Number
1
Number of Pages
XII, 325
Number of Illustrations
90 b/w illustrations
Topics