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Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems

Theory, Algorithm, and Applications

  • Book
  • © 2001

Overview

Authors:
  1. Jens Lang

    1. Konrad-Zuse-Zentrum Berlin, Berlin-Dahlem, Germany

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  • Monograph on a hot topic in CSE
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 16)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XII
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  2. Introduction

    • Jens Lang
    Pages 1-4

  3. The Continuous Problem and Its Discretization in Time

    • Jens Lang
    Pages 5-13

  4. Convergence of the Discretization in Time and Space

    • Jens Lang
    Pages 15-29

  5. Computational Error Estimation

    • Jens Lang
    Pages 31-45

  6. Towards an Effective Algorithm. Practical Issues

    • Jens Lang
    Pages 47-68

  7. Illustrative Numerical Tests

    • Jens Lang
    Pages 69-77

  8. Applications from Computational Sciences

    • Jens Lang
    Pages 79-117

  9. Back Matter

    Pages 119-162
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Keywords

About this book

Nowadays there is an increasing emphasis on all aspects of adaptively gener­ ating a grid that evolves with the solution of a PDE. Another challenge is to develop efficient higher-order one-step integration methods which can handle very stiff equations and which allow us to accommodate a spatial grid in each time step without any specific difficulties. In this monograph a combination of both error-controlled grid refinement and one-step methods of Rosenbrock-type is presented. It is my intention to impart the beauty and complexity found in the theoretical investigation of the adaptive algorithm proposed here, in its realization and in solving non-trivial complex problems. I hope that this method will find many more interesting applications. Berlin-Dahlem, May 2000 Jens Lang Acknowledgements I have looked forward to writing this section since it is a pleasure for me to thank all friends who made this work possible and provided valuable input. I would like to express my gratitude to Peter Deuflhard for giving me the oppor­ tunity to work in the field of Scientific Computing. I have benefited immensly from his help to get the right perspectives, and from his continuous encourage­ ment and support over several years. He certainly will forgive me the use of Rosenbrock methods rather than extrapolation methods to integrate in time.

Authors and Affiliations

  • Konrad-Zuse-Zentrum Berlin, Berlin-Dahlem, Germany

    Jens Lang

Bibliographic Information

  • Book Title: Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems

  • Book Subtitle: Theory, Algorithm, and Applications

  • Authors: Jens Lang

  • Series Title: Lecture Notes in Computational Science and Engineering

  • DOI: https://doi.org/10.1007/978-3-662-04484-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2001

  • Hardcover ISBN: 978-3-540-67900-4Published: 16 November 2000

  • Softcover ISBN: 978-3-642-08747-9Published: 07 December 2010

  • eBook ISBN: 978-3-662-04484-1Published: 29 June 2013

  • Series ISSN: 1439-7358

  • Series E-ISSN: 2197-7100

  • Edition Number: 1

  • Number of Pages: XII, 162

  • Number of Illustrations: 52 b/w illustrations

  • Topics: Theory of Computation, Analysis, Numerical Analysis

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