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Elliptic Differential Equations

Theory and Numerical Treatment

  • Wolfgang Hackbusch

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 18)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Wolfgang Hackbusch
    Pages 13-28
  3. Wolfgang Hackbusch
    Pages 29-42
  4. Wolfgang Hackbusch
    Pages 43-91
  5. Wolfgang Hackbusch
    Pages 93-118
  6. Wolfgang Hackbusch
    Pages 119-158
  7. Wolfgang Hackbusch
    Pages 159-180
  8. Wolfgang Hackbusch
    Pages 181-262
  9. Wolfgang Hackbusch
    Pages 263-310
  10. Wolfgang Hackbusch
    Pages 311-327
  11. Wolfgang Hackbusch
    Pages 329-354
  12. Wolfgang Hackbusch
    Pages 355-380
  13. Back Matter
    Pages 381-455

About this book

Introduction

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

Keywords

difference methods elliptic boundary value problems finite elements methods variational formulation eigenvalue problems

Authors and affiliations

  • Wolfgang Hackbusch
    • 1
  1. 1.MPI für Mathematik in den NaturwissenschaftenLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-54961-2
  • Copyright Information Springer-Verlag GmbH Germany 2017
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-662-54960-5
  • Online ISBN 978-3-662-54961-2
  • Series Print ISSN 0179-3632
  • Series Online ISSN 2198-3712
  • Buy this book on publisher's site