Mathematical Aspects of Discontinuous Galerkin Methods

  • Daniele Antonio Di Pietro
  • Alexandre Ern
Part of the Mathématiques et Applications book series (MATHAPPLIC, volume 69)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Daniele Antonio Di Pietro, Alexandre Ern
    Pages 1-34
  3. Scalar First-Order PDEs

    1. Front Matter
      Pages 35-35
  4. Scalar first order PDEs

    1. Daniele Antonio Di Pietro, Alexandre Ern
      Pages 37-65
    2. Daniele Antonio Di Pietro, Alexandre Ern
      Pages 67-115
  5. Scalar Second-Order PDEs

    1. Front Matter
      Pages 117-117
  6. Scalar second order PDEs

    1. Daniele Antonio Di Pietro, Alexandre Ern
      Pages 119-186
    2. Daniele Antonio Di Pietro, Alexandre Ern
      Pages 187-237
  7. Systems

    1. Front Matter
      Pages 239-239
    2. Daniele Antonio Di Pietro, Alexandre Ern
      Pages 241-291
    3. Daniele Antonio Di Pietro, Alexandre Ern
      Pages 293-341
  8. Back Matter
    Pages 343-384

About this book

Introduction

This book introduces the basic ideas for building discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. It is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite-element and finite-volume viewpoints are utilized to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.

Keywords

Discontinuous Galerkin methods First-order PDEs Friedrichs' systems Incompressible Navier-Stokes equations Second-order PDEs

Authors and affiliations

  • Daniele Antonio Di Pietro
    • 1
  • Alexandre Ern
    • 2
  1. 1., Department of Applied MathematicsIFP Energies nouvellesRueil-MalmaisonFrance
  2. 2., CERMICS, Ecole des Ponts ParisTechUniversité Paris EstMarne la Vallée cedex 2France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-22980-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-22979-4
  • Online ISBN 978-3-642-22980-0
  • Series Print ISSN 1154-483X
  • About this book