Numerical Methods and Analysis of Multiscale Problems
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Beschreibung
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.
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
Autor*in
Alexandre L. Madureira
Themen in »Numerical Methods and Analysis of Multiscale Problems«
Asymptotic Analysis Elliptic Equations Finite Elements Multiscale Singular Perturbed Problems partial differential equations
Stimmen zu »Numerical Methods and Analysis of Multiscale Problems«
“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)
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