Advertisement

Galerkin Finite Element Methods for Parabolic Problems

  • Vidar Thomée

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 25)

Table of contents

  1. Front Matter
    Pages I-X
  2. Vidar Thomée
    Pages 1-22
  3. Vidar Thomée
    Pages 35-50
  4. Vidar Thomée
    Pages 51-62
  5. Vidar Thomée
    Pages 63-80
  6. Vidar Thomée
    Pages 145-162
  7. Vidar Thomée
    Pages 209-222
  8. Vidar Thomée
    Pages 223-238
  9. Vidar Thomée
    Pages 239-252
  10. Vidar Thomée
    Pages 253-266
  11. Vidar Thomée
    Pages 267-278
  12. Vidar Thomée
    Pages 279-287
  13. Back Matter
    Pages 289-302

About this book

Introduction

My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.

Keywords

Approximation Differential Equations Finite Element Theory Galerkin Methods Parabolic Partial algebra differential equation finite element method mathematics maximum

Authors and affiliations

  • Vidar Thomée
    • 1
  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03359-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-03361-6
  • Online ISBN 978-3-662-03359-3
  • Series Print ISSN 0179-3632
  • Buy this book on publisher's site