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Numerical Approximation of Partial Differential Equations

  • Textbook
  • © 2016

Overview

Authors:
  1. Sören Bartels

    1. Angewandte Mathematik, Albert-Ludwigs-Universitaet, Freiburg, Germany

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  • Matlab implementations illustrate the devised methods
  • Problems, projects, and quizzes allow for self-evaluation
  • Includes theoretical and physical backgrounds of mathematical models

Part of the book series: Texts in Applied Mathematics (TAM, volume 64)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xv
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  2. Finite Differences and Finite Elements

    1. Front Matter

      Pages 1-1
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    2. Finite Difference Method

      • Sören Bartels
      Pages 3-64

    3. Elliptic Partial Differential Equations

      • Sören Bartels
      Pages 65-97

    4. Finite Element Method

      • Sören Bartels
      Pages 99-152

  3. Local Resolution and Iterative Solution

    1. Front Matter

      Pages 153-153
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    2. Local Resolution Techniques

      • Sören Bartels
      Pages 155-207

    3. Iterative Solution Methods

      • Sören Bartels
      Pages 209-244

  4. Constrained and Singularly Perturbed Problems

    1. Front Matter

      Pages 245-245
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    2. Saddle-Point Problems

      • Sören Bartels
      Pages 247-281

    3. Mixed and Nonstandard Methods

      • Sören Bartels
      Pages 283-347

    4. Applications

      • Sören Bartels
      Pages 349-404

  5. Back Matter

    Pages 405-535
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Keywords

About this book

Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.

Authors and Affiliations

  • Angewandte Mathematik, Albert-Ludwigs-Universitaet, Freiburg, Germany

    Sören Bartels

About the author

Sören Bartels is Professor of Applied Mathematics at the Albert-Ludwigs University in Freiburg, Germany. His primary research interest is in the development and analysis of approximation schemes for nonlinear partial differential equations with applications in the simulation of modern materials. Professor Bartels has published the Springer textbook "Numerik 3x9" and the monograph "Numerical methods for nonlinear partial differential equations" in the Springer Series in Computational Mathematics.

Bibliographic Information

  • Book Title: Numerical Approximation of Partial Differential Equations

  • Authors: Sören Bartels

  • Series Title: Texts in Applied Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-32354-1

  • Publisher: Springer Cham

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

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-32353-4Published: 09 June 2016

  • Softcover ISBN: 978-3-319-81265-6Published: 30 May 2018

  • eBook ISBN: 978-3-319-32354-1Published: 02 June 2016

  • Series ISSN: 0939-2475

  • Series E-ISSN: 2196-9949

  • Edition Number: 1

  • Number of Pages: XV, 535

  • Number of Illustrations: 170 b/w illustrations

  • Topics: Numerical Analysis, Partial Differential Equations

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