Texts in Applied Mathematics

Numerical Approximation of Partial Differential Equations

Authors: Bartels, Sören

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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
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  • ISBN 978-3-319-32354-1
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About this Textbook

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.

About the authors

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.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-3-319-32354-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-319-32353-4
  • with online files
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $74.99
price for USA in USD
  • ISBN 978-3-319-81265-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Approximation of Partial Differential Equations
Authors
Series Title
Texts in Applied Mathematics
Series Volume
64
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-32354-1
DOI
10.1007/978-3-319-32354-1
Hardcover ISBN
978-3-319-32353-4
Softcover ISBN
978-3-319-81265-6
Series ISSN
0939-2475
Edition Number
1
Number of Pages
XV, 535
Number of Illustrations
170 b/w illustrations
Topics