Robust Numerical Methods for Singularly Perturbed Differential Equations

Convection-Diffusion-Reaction and Flow Problems

  • Hans-Görg Roos
  • Martin Stynes
  • Lutz Tobiska

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 24)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Ordinary Differential Equations

  3. Parabolic Initial-Boundary Value Problems in One Space Dimension

    1. Front Matter
      Pages 151-153
    2. Pages 155-157
    3. Pages 195-221
    4. Pages 223-229
  4. Elliptic and Parabolic Problems in Several Space Dimensions

    1. Front Matter
      Pages 231-233
    2. Pages 277-425
    3. Pages 427-442
  5. The Incompressible Navier-Stokes Equations

About this book


This considerably extended and completely revised second edition incorporates many new developments in the thriving field of numerical methods for singularly perturbed differential equations. It provides a thorough foundation for the numerical analysis and solution of these problems, which model many physical phenomena whose solutions exhibit layers. The book focuses on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics. It offers a comprehensive overview of suitable numerical methods while emphasizing those with realistic error estimates. The book should be useful for scientists requiring effective numerical methods for singularly perturbed differential equations.


Boundary value problem Navier-stokes equations Singular perturbation boundary and interior layers convection-diffusion differential equation finite element method layer-adapted grids layers model numerical analysis numerical methods stabilised finite elements variational multiscale approach

Authors and affiliations

  • Hans-Görg Roos
    • 1
  • Martin Stynes
    • 2
  • Lutz Tobiska
    • 3
  1. 1.Fakultät Mathematik und Naturwissenschaften Institut für Numerische MathematikTechnische Universität DresdenDresdenGermany
  2. 2.Department of MathematicsUniversity College CorkCorkIreland
  3. 3.Fakultät für Mathematik Institut für Analysis und NumerikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-34466-7
  • Online ISBN 978-3-540-34467-4
  • Series Print ISSN 0179-3632
  • About this book