Authors:
- Short chapters allow for development of ideas in a classroom setting
- Many exercises and hints included
- Well adapted for graduate flipped classes
- Part of a three volume work
Part of the book series: Texts in Applied Mathematics (TAM, volume 74)
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Table of contents (28 chapters)
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Front Matter
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Time-dependent Stokes equations
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Front Matter
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About this book
This book is the third 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 III is divided into 28 chapters. The first eight chapters focus on the symmetric positive systems of first-order PDEs called Friedrichs' systems. This part of the book presents a comprehensive and unified treatment of various stabilization techniques from the existing literature. It discusses applications to advection and advection-diffusion equations and various PDEs written in mixed form such as Darcy and Stokes flows and Maxwell's equations. The remainder of Volume III addresses time-dependent problems: parabolic equations (such as the heat equation), evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear hyperbolic equations (scalar conservation equations, hyperbolic systems). It offers a fresh perspective on the analysis of well-known time-stepping methods. The last five chapters discuss the approximation of hyperbolic equations with finite elements. Here again a new perspective is proposed. These chapters should convince the reader that finite elements offer a good alternative to finite volumes to solve nonlinear conservation equations.Authors and Affiliations
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CERMICS, Ecole des Ponts and INRIA Paris, Marne la Vallée and Paris, France
Alexandre Ern
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Department of Mathematics, Texas A&M University, College Station, USA
Jean-Luc Guermond
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 III
Book Subtitle: First-Order and Time-Dependent PDEs
Authors: Alexandre Ern, Jean-Luc Guermond
Series Title: Texts in Applied Mathematics
DOI: https://doi.org/10.1007/978-3-030-57348-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-57347-8Published: 30 March 2021
Softcover ISBN: 978-3-030-57349-2Published: 30 March 2022
eBook ISBN: 978-3-030-57348-5Published: 29 March 2021
Series ISSN: 0939-2475
Series E-ISSN: 2196-9949
Edition Number: 1
Number of Pages: VIII, 417
Number of Illustrations: 16 b/w illustrations
Topics: Analysis, Functional Analysis