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Numerical Methods for Elliptic and Parabolic Partial Differential Equations

  • Textbook
  • © 2003

Overview

Authors:
  1. Peter Knabner

    1. Institute for Applied Mathematics, University of Erlangen, Erlangen, Germany

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    You can also search for this author in PubMed   Google Scholar

  2. Lutz Angermann

    1. Institute for Mathematics, University of Clausthal, Clausthal-Zellerfeld, Germany

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Texts in Applied Mathematics (TAM, volume 44)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xv
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  2. For Example: Modelling Processes in Porous Media with Differential Equations

    Pages 1-18

  3. For the Beginning: The Finite Difference Method for the Poisson Equation

    Pages 19-45

  4. The Finite Element Method for the Poisson Equation

    Pages 46-91

  5. The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order

    Pages 92-175

  6. Grid Generation and A Posteriori Error Estimation

    Pages 176-197

  7. Iterative Methods for Systems of Linear Equations

    Pages 198-254

  8. The Finite Volume Method

    Pages 255-282

  9. Discretization Methods for Parabolic Initial Boundary Value Problems

    Pages 283-341

  10. Iterative Methods for Nonlinear Equations

    Pages 342-367

  11. Discretization Methods for Convection-Dominated Problems

    Pages 368-389

  12. Back Matter

    Pages 390-424
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Keywords

About this book

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in - search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, whichwill focus on advanced textbooks and research-level monographs.

Authors and Affiliations

  • Institute for Applied Mathematics, University of Erlangen, Erlangen, Germany

    Peter Knabner

  • Institute for Mathematics, University of Clausthal, Clausthal-Zellerfeld, Germany

    Lutz Angermann

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