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The aim of this monograph is to describe the main concepts and
recent - vances in multiscale ?nite element methods. This monograph
is intended for
thebroaderaudienceincludingengineers,appliedscientists,andforthosewho
are interested in multiscale simulations. The book is intended for
graduate students in applied mathematics and those interested in
multiscale compu- tions. It combines a practical introduction,
numerical results, and analysis of multiscale ?nite element
methods. Due to the page limitation, the material has been
condensed. Each chapter of the book starts with an introduction and
description of the proposed methods and motivating examples. Some
new techniques are introduced using formal arguments that are
justi?ed later in the last chapter. Numerical examples
demonstrating the signi?cance of the proposed methods are presented
in each chapter following the description of the methods. In the
last chapter, we analyze a few representative cases with the
objective of demonstrating the main error sources and the
convergence of the proposed methods. A brief outline of the book is
as follows. The ?rst chapter gives a general
introductiontomultiscalemethodsandanoutlineofeachchapter.Thesecond
chapter discusses the main idea of the multiscale ?nite element
method and its extensions. This chapter also gives an overview of
multiscale ?nite element methods and other related methods. The
third chapter discusses the ext- sion of multiscale ?nite element
methods to nonlinear problems. The fourth chapter focuses on
multiscale methods that use limited global information.
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