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Theory and Practice of Finite Elements

  • Alexandre Ern
  • Jean-Luc Guermond

Part of the Applied Mathematical Sciences book series (AMS, volume 159)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Theoretical Foundations

    1. Front Matter
      Pages 1-1
    2. Alexandre Ern, Jean-Luc Guermond
      Pages 3-80
    3. Alexandre Ern, Jean-Luc Guermond
      Pages 81-108
  3. Approximation of PDEs

    1. Front Matter
      Pages 109-109
    2. Alexandre Ern, Jean-Luc Guermond
      Pages 111-174
    3. Alexandre Ern, Jean-Luc Guermond
      Pages 175-217
    4. Alexandre Ern, Jean-Luc Guermond
      Pages 219-278
    5. Alexandre Ern, Jean-Luc Guermond
      Pages 279-334
  4. Implementation

    1. Front Matter
      Pages 335-335
    2. Alexandre Ern, Jean-Luc Guermond
      Pages 337-356
    3. Alexandre Ern, Jean-Luc Guermond
      Pages 357-382
    4. Alexandre Ern, Jean-Luc Guermond
      Pages 383-419
    5. Alexandre Ern, Jean-Luc Guermond
      Pages 421-460
  5. Back Matter
    Pages 461-526

About this book

Introduction

This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation.

The body of the text is organized into three parts plus two appendices collecting the functional analysis  results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of inf-sup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, first-order PDEs, and the time-dependent versions of these problems. The third part covers implementation issues and should provide readers with  most of  the practical details needed to write or understand a finite element code.

Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences.

The book will be useful to researchers and graduate students in mathematics, computer science and engineering.

Keywords

Galerkin approximation Sobolev space algorithms calculus finite element method finite elements numerical analysis partial differential equations

Authors and affiliations

  • Alexandre Ern
    • 1
  • Jean-Luc Guermond
    • 2
  1. 1.CERMICS, ENPCMarne la Vallée cedex 2France
  2. 2.LIMSI, CNRSOrsay cedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4355-5
  • Copyright Information Springer-Verlag New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-1918-2
  • Online ISBN 978-1-4757-4355-5
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site
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