Titlebook: Numerical Methods and Analysis of Multiscale Problems; Alexandre L. Madureira Book 2017 The Author(s) 2017 Asymptotic Analysis.Elliptic Eq

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annexation

Modeling PDEs in Domains with Rough Boundaries, For a general domain, a possibility is to use a domain decomposition approach, solving local problems in parallel in the spirit of the Multiscale Finite Element Method. Asymptotic expansions play a key role in both alternatives, motivating the development of models, and helping in deriving error estimates.

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Book 2017diffusion 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..

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2191-8198 dies on modeling techniques of multiscale PDEs, in one- and .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

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Book 2017 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 ma

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An Application in Neuroscience: Heterogeneous Cable Equation,estigated in Chap.?. Moreover, other interesting asymptotics arise when considering a large number of synapses..We also show here that the Multiscale Finite Element Method yields good approximations under all asymptotic regimes, even when the Galerkin Method fails.