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

### Yalchin Efendiev; Thomas Y. Hou

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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.

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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.

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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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Book Description Springer-Verlag New York Inc., United States, 2009. Paperback. Book Condition: New. 2009 ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New 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. Bookseller Inventory # LIE9780387094953

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Book Description Springer-Verlag New York Inc., United States, 2009. Paperback. Book Condition: New. 2009 ed.. Language: English . Brand New Book ***** Print on Demand *****. 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. Bookseller Inventory # AAV9780387094953

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Book Description Springer-Verlag New York Inc., United States, 2009. Paperback. Book Condition: New. 2009.. Language: English . Brand New Book ***** Print on Demand *****.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. Bookseller Inventory # AAV9780387094953

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Book Description Springer. Paperback. Book Condition: New. 234 pages. Dimensions: 9.1in. x 6.0in. x 0.6in.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 justied later in the last chapter. Numerical examples demonstrating the signicance 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Bookseller Inventory # 9780387094953

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