Numerical Methods and Analysis of Multiscale Problems

  • Alexandre L. Madureira

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Alexandre L. Madureira
    Pages 1-21
  3. Alexandre L. Madureira
    Pages 23-38
  4. Alexandre L. Madureira
    Pages 49-65
  5. Alexandre L. Madureira
    Pages 67-84
  6. Back Matter
    Pages 109-123

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.


Asymptotic Analysis Elliptic Equations Finite Elements Multiscale Singular Perturbed Problems

Authors and affiliations

  • Alexandre L. Madureira
    • 1
  1. 1.Laboratório Nacional de Computação Científica-LNCCPetrópolisBrazil

Bibliographic information