SpringerBriefs in Mathematics

Numerical Methods and Analysis of Multiscale Problems

Authors: Madureira, Alexandre L

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  • Offers an introduction to asymptotic analysis techniques and various finite element methods for elliptic problems
  • Presents numerous case studies on modeling techniques of multiscale PDEs, in one- and two-dimensional domains
  • Explores modeling through both continuous and numerical approximations
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  • ISBN 978-3-319-50866-5
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About this book

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales.  Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses  examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods.

The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.


About the authors

Alexandre L. Madureira is a senior researcher at the National Laboratory for Scientific Computing (LNCC), Brazil, and also works at the Brazilian School of Economics and Finance (EPGE) at the Fundação Getúlio Vargas (FGV). He holds a PhD from Penn State University, USA, and served as a visiting professor at the Istituto di Analisi Numerica (IAN), Italy, University of Colorado at Denver, USA, and Brown University, USA. His main field of interest is numerical analysis, more specifically modeling and analysis of multiscale problems from PDE and numerical points of view.

Reviews

“This book is a tutorial on numerical methods for multiscale problems accompanied by the corresponding numerical analysis. It is well studied as introductory material for graduate students at the master's level. ... All proofs are given in detail and results of instructive numerical experiments are demonstrated.” (Karsten Urban, Mathematical Reviews, May, 2018)

“This monograph is concerned with the asymptotic analysis and numerical methods for multiscale problems. … the book is orientated toward advanced undergraduate and graduate students.” (Rolf Dieter Grigorieff, zbMATH, Vol. 1366.65108, 2017)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook n/a
  • ISBN 978-3-319-50866-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
Softcover n/a
  • ISBN 978-3-319-50864-1
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Methods and Analysis of Multiscale Problems
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-50866-5
DOI
10.1007/978-3-319-50866-5
Softcover ISBN
978-3-319-50864-1
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 123
Number of Illustrations
22 b/w illustrations, 9 illustrations in colour
Topics