Multiscale Finite Element Methods: Theory and Applications (Surveys and Tutorials in the Applied Mathematical Sciences, Vol. 4)

Efendiev, Yalchin

ISBN 10: 0387094954 / ISBN 13: 9780387094953

Published by Springer, 2009

About this Item

The book is in good condition with all pages and cover intact, including the dust jacket if originally issued. The spine may show light wear. Pages may contain some notes or highlighting, and there might be a "From the library of" label. Boxed set packaging, shrink wrap, or included media like CDs may be missing. Seller Inventory # BSM.KA2P

Bibliographic Details

Title: Multiscale Finite Element Methods: Theory ...

Publisher: Springer

Publication Date: 2009

Binding: Soft cover

Condition: good

About this title

Synopsis:

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.

From the Back Cover:

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.