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 informatio
