Authors:
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
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.
Reviews
“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)
Authors and Affiliations
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Laboratório Nacional de Computação Científica-LNCC, Petrópolis, Brazil
Alexandre L. Madureira
About the author
Bibliographic Information
Book Title: Numerical Methods and Analysis of Multiscale Problems
Authors: Alexandre L. Madureira
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-50866-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2017
Softcover ISBN: 978-3-319-50864-1Published: 23 February 2017
eBook ISBN: 978-3-319-50866-5Published: 15 February 2017
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: X, 123
Number of Illustrations: 22 b/w illustrations, 9 illustrations in colour
Topics: Numerical Analysis, Partial Differential Equations, Applications of Mathematics