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Springer Series in Computational Mathematics

Galerkin Finite Element Methods for Parabolic Problems

Authors: Thomee, Vidar

  • This book is the most comprehensive and reliable book on the topic and will become the standard reference.

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  • ISBN 978-3-662-03359-3
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About this book

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.

Table of contents (18 chapters)

  • The Standard Galerkin Method

    Thomée, Vidar

    Pages 1-22

  • Methods Based on More General Approximations of the Elliptic Problem

    Thomée, Vidar

    Pages 23-34

  • Nonsmooth Data Error Estimates

    Thomée, Vidar

    Pages 35-50

  • More General Parabolic Equations

    Thomée, Vidar

    Pages 51-62

  • Maximum-Norm Stability and Error Estimates

    Thomée, Vidar

    Pages 63-80

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-3-662-03359-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Galerkin Finite Element Methods for Parabolic Problems
Authors
Series Title
Springer Series in Computational Mathematics
Series Volume
25
Copyright
1997
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-03359-3
DOI
10.1007/978-3-662-03359-3
Series ISSN
0179-3632
Edition Number
1
Number of Pages
X, 302
Topics