Numerical Methods and Analysis of Multiscale Problems

Front Cover
Springer, Feb 15, 2017 - Mathematics - 123 pages

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.


 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

1 Introductory Material and Finite Element Methods
1
2 OneDimensional Singular Perturbed Problems
22
Heterogeneous Cable Equation
39
4 TwoDimensional ReactionDiffusion Equations
49
5 Modeling PDEs in Domains with Rough Boundaries
66
6 Partial Differential Equations with Oscillatory Coefficients
85
References
109
Index
121
Copyright

Other editions - View all

Common terms and phrases

About the author (2017)

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.

Bibliographic information