Multiscale finite element methods: Theory and applications

Thomas Hou, Yalchin Efendiev (auth.)9780387094953, 9780387094960, 0387094954, 0387094962

This expository book surveys the main concepts and recent advances in multiscale finite element methods. This monograph is intended for the broader audiences including engineers, applied scientists and those who are interested in multiscale simulations. The book is self-contained, starts from the basic concepts and proceeds to the latest developments in the field.

Each chapter of the book starts with a simple introduction and the description of the proposed methods as well as with motivating examples. Numerical examples demonstrating the significance of the proposed methods are presented in each chapter. The book addresses mathematical and numerical issues in multiscale finite element methods and connects them to real-world applications. Narrative introduction provides a key to the
book’s organization and its scope. To make the presentation accessible to a broader audience, the analyses of the methods are given in the last chapter.

Yalchin Efendiev is a Professor at Texas A&M University in College Station, Texas and Thomas Hou is the Charles Lee Powell Professor at California Institute of Technology in Pasadena, California.

Table of contents :
Front Matter….Pages 1-11
Introduction….Pages 1-12
Multiscale finite element methods for linear problems and overview….Pages 1-34
Multiscale finite element methods for nonlinear equations….Pages 1-20
Multiscale ¯nite element methods using limited global information….Pages 1-28
Applications of multiscale ¯nite element methods….Pages 1-69
Analysis….Pages 1-37
Back Matter….Pages 1-30