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Multiscale Finite Element Methods

Theory and Applications

  • Textbook
  • © 2009

Overview

Authors:
  1. Thomas Hou
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    You can also search for this author in PubMed   Google Scholar

  2. Yalchin Efendiev
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  • Simple introductions and descriptions at the beginning of each chapter
  • Short, user-friendly narrative approach suitable for engineers
  • Combines practical introduction, numerical results and analysis of multiscale finite element methods
  • Includes supplementary material: sn.pub/extras

Part of the book series: Surveys and Tutorials in the Applied Mathematical Sciences (STAMS, volume 4)

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Table of contents (6 chapters)

  1. Front Matter

    Pages 1-11
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  2. Introduction

    Pages 1-12

  3. Multiscale finite element methods for linear problems and overview

    Pages 1-34

  4. Multiscale finite element methods for nonlinear equations

    Pages 1-20

  5. Multiscale ¯nite element methods using limited global information

    Pages 1-28

  6. Applications of multiscale ¯nite element methods

    Pages 1-69

  7. Analysis

    Pages 1-37

  8. Back Matter

    Pages 1-30
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Keywords

About this book

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.

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)

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