Multiscale Finite Element Methods: Theory and Applications by Yalchin EfendievMultiscale Finite Element Methods: Theory and Applications by Yalchin Efendiev

Multiscale Finite Element Methods: Theory and Applications

byYalchin Efendiev, Thomas Y. Hou

Paperback | February 5, 2009

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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.
Title:Multiscale Finite Element Methods: Theory and ApplicationsFormat:PaperbackDimensions:234 pagesPublished:February 5, 2009Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387094954

ISBN - 13:9780387094953

Reviews

Table of Contents

Multiscale finite element methods for linear problems and overview.- Multiscale finite element methods for nonlinear equations.- Multiscale ¯nite element methods using limited global information.- Applications of multiscale ¯nite element methods.- Analysis.

Editorial Reviews

From the reviews:"This book describes the main concepts and various applications of the multiscale finite element method (MsFEM). . This monograph is intended for engineers, graduate students, and applied scientists who are interested in multiscale simulations. . In this book, the authors chose to focus on the extensions of MsFEM and its applications. . Overall, the book is an interesting read presenting an overview of MsFEM and the wide range of applications handled by MsFEM." (Ulrich Hetmaniuk, SIAM Review, Vol. 53 (2), 2011)