Read While You Wait - Get immediate ebook access, if available*, when you order a print book

Texts in Applied Mathematics
cover

Finite Elements II

Galerkin Approximation, Elliptic and Mixed PDEs

Authors: Ern, Alexandre, Guermond, Jean-Luc

  • 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
see more benefits

Buy this book

eBook 54,99 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: December 2, 2020
  • ISBN 978-3-030-56923-5
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 67,59 €
price for Spain (gross)
  • Due: December 2, 2020
  • ISBN 978-3-030-56922-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This book is the second 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 II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows).  Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.

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 peerreviewed journals. He has supervised about 20 PhD students and 10 postdoctoral 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.

Buy this book

eBook 54,99 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: December 2, 2020
  • ISBN 978-3-030-56923-5
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 67,59 €
price for Spain (gross)
  • Due: December 2, 2020
  • ISBN 978-3-030-56922-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Finite Elements II
Book Subtitle
Galerkin Approximation, Elliptic and Mixed PDEs
Authors
Series Title
Texts in Applied Mathematics
Series Volume
73
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-56923-5
DOI
10.1007/978-3-030-56923-5
Hardcover ISBN
978-3-030-56922-8
Series ISSN
0939-2475
Edition Number
1
Number of Pages
IX, 478
Number of Illustrations
23 b/w illustrations, 1 illustrations in colour
Topics

*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works and instructor copies are not included.