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Numerical Treatment of Partial Differential Equations

  • Textbook
  • © 2007
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Overview

Authors:
  1. Christian Grossmann

    1. Technical University of Dresden, D-01062, Germany

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  2. Hans-Gorg Roos

    1. Technical University of Dresden, D-01062, Germany

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  3. Martin Stynes

    1. University College Cork, Ireland

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Part of the book series: Universitext (UTX)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XII
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  2. Partial Differential Equations: Basics and Explicit Representation of Solutions

    Pages 1-21
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  3. Finite Difference Methods

    Pages 23-124
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  4. Weak Solutions, Elliptic Problems and Sobolev Spaces

    Pages 125-172
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  5. The Finite Element Method

    Pages 173-315
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  6. Finite Element Methods for Unsteady Problems

    Pages 317-373
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  7. Singular Perturbations

    Pages 375-434
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  8. Numerical Methods for Variational Inequalities and Optimal Control

    Pages 435-498
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  9. Numerical Methods for Discretized Problems

    Pages 499-569
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  10. Back Matter

    Pages 571-591
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Keywords

About this book

Many well-known models in the natural sciences and engineering, and today even in economics, depend on partial di?erential equations. Thus the e?cient numerical solution of such equations plays an ever-increasing role in state-- the-art technology. This demand and the computational power available from current computer hardware have together stimulated the rapid development of numerical methods for partial di?erential equations—a development that encompasses convergence analyses and implementational aspects of software packages. In 1988 we started work on the ?rst German edition of our book, which appeared in 1992. Our aim was to give students a textbook that contained the basic concepts and ideas behind most numerical methods for partial di?er- tial equations. The success of this ?rst edition and the second edition in 1994 encouraged us, ten years later, to write an almost completely new version, taking into account comments from colleagues and students and drawing on the enormous progress made in the numerical analysis of partial di?erential equations in recent times. The present English version slightly improves the third German edition of 2005: we have corrected some minor errors and added additional material and references.

Reviews

From the reviews:

"This textbook is the translation and revision of the third German edition of 2005. ... the book deals with different aspects of the numerical solution of elliptic, parabolic and hyperbolic partial differential equations. ... An index and two pages with a summary of the notations used complete the presentation. ... It can be highly recommended for students and engineers but also for numerical analysts." (Riidiger Weiner, Zentralblatt fiir Angewandte Mathematik and Mechanik, Vol. 88 (12), 2008)

Authors and Affiliations

  • Technical University of Dresden, D-01062, Germany

    Christian Grossmann, Hans-Gorg Roos

  • University College Cork, Ireland

    Martin Stynes

Bibliographic Information

  • Book Title: Numerical Treatment of Partial Differential Equations

  • Authors: Christian Grossmann, Hans-Gorg Roos, Martin Stynes

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-540-71584-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2007

  • Softcover ISBN: 978-3-540-71582-5Published: 04 October 2007

  • eBook ISBN: 978-3-540-71584-9Published: 11 August 2007

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XII, 596

  • Number of Illustrations: 86 b/w illustrations

  • Additional Information: Translation and Revision of the 3rd edition of "Numerische Behandlung partieller Differentialgleichungen" published by Teubner, 2005

  • Topics: Analysis, Numerical Analysis, Partial Differential Equations

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