The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics)

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9780387759333: The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics)

This is the third and yet further updated edition of a highly regarded mathematical text. Brenner develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. Her volume formalizes basic tools that are commonly used by researchers in the field but not previously published. The book is ideal for mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. This new edition is substantially updated with additional exercises throughout and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes.

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From the Back Cover:

This book develops the basic mathematical theory of the finite element  method, the most widely used technique for engineering design and analysis.

The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara\'e-Friedrichs inequalities for piecewise W^1_p functions. New exercises have also been added throughout.

The initial chapter provides an introducton to the entire subject, developed in the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to:

 - multigrid methods and domain decomposition methods

 - mixed methods with applications to elasticity and fluid mechanics

 - iterated penalty and augmented Lagrangian methods

 - variational "crimes" including nonconforming and isoparametric  methods, numerical integration and interior penalty methods

 - error estimates in the maximum norm with applications to nonlinear problems

 - error estimators, adaptive meshes and convergence analysis of an adaptive algorithm

- Banach-space operator-interpolation techniques

The book has proved useful to mathematicians as well as engineers and  physical scientists. It can be used for a course that provides an  introduction to basic functional analysis, approximation theory and  numerical analysis, while building upon and applying basic techniques of real variable theory. It can also be used for courses that emphasize physical applications or algorithmic efficiency.

Reviews of earlier editions: "This book represents an important contribution to the mathematical literature of finite elements. It is both a well-done text and a good reference." (Mathematical Reviews, 1995)

"This is an excellent, though demanding, introduction to key mathematical topics in the finite element method, and at the same time a valuable reference and source for workers in the area."

 (Zentralblatt,  2002)

 

Review:

Second Edition

S.C. Brenner and L.R. Scott

The Mathematical Theory of Finite Element Methods

"[This is] a well-written book. A great deal of material is covered, and students who have taken the trouble to master at least some of the advanced material in the later chapters would be well placed to embark on research in the area."

ZENTRALBLATT MATH

From the reviews of the third edition:

"An excelent survey of the deep mathematical roots of finite element methods as well as of some of the newest and most formal results concerning these methods. ... The approach remains very clear and precise ... . A significant number of examples and exercises improve considerably the accessability of the text. The authors also point out different ways the book could be used in various courses. ... valuable reference and source for researchers (mainly mathematicians) in the topic." (Calin Ioan Gheorghiu, Zentralblatt MATH, Vol. 1135 (13), 2008)

"Sobre este título" puede pertenecer a otra edición de este libro.

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Brenner, Susanne, Scott, Ridgway
Editorial: Springer (2007)
ISBN 10: 0387759336 ISBN 13: 9780387759333
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Descripción Springer, 2007. Estado de conservación: New. This is the third and yet further updated edition of a highly regarded mathematical text. Brenner develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. Series: Texts in Applied Mathematics. Num Pages: 418 pages, biography. BIC Classification: PBW. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 235 x 164 x 31. Weight in Grams: 762. . 2007. 3rd. Hardcover. . . . . . Nº de ref. de la librería V9780387759333

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Susanne C. Brenner, Ridgway Scott
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ISBN 10: 0387759336 ISBN 13: 9780387759333
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Descripción Springer-Verlag New York Inc., United States, 2008. Hardback. Estado de conservación: New. 3rd ed. 2008. Language: English . Brand New Book. This is the third and yet further updated edition of a highly regarded mathematical text. Brenner develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. Her volume formalizes basic tools that are commonly used by researchers in the field but not previously published. The book is ideal for mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. This new edition is substantially updated with additional exercises throughout and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes. Nº de ref. de la librería AAU9780387759333

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Susanne Brenner, Ridgway Scott
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Descripción Springer New York 2007-12-14, New York, NY, 2007. hardback. Estado de conservación: New. Nº de ref. de la librería 9780387759333

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Descripción Springer-Verlag New York Inc., United States, 2008. Hardback. Estado de conservación: New. 3rd ed. 2008. Language: English . Brand New Book. This is the third and yet further updated edition of a highly regarded mathematical text. Brenner develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. Her volume formalizes basic tools that are commonly used by researchers in the field but not previously published. The book is ideal for mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. This new edition is substantially updated with additional exercises throughout and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes. Nº de ref. de la librería AAU9780387759333

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Susanne Brenner; Ridgway Scott
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Descripción Springer, 2007. Estado de conservación: New. book. Nº de ref. de la librería ria9780387759333_rkm

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Descripción Springer. Estado de conservación: New. This is the third and yet further updated edition of a highly regarded mathematical text. Brenner develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. Series: Texts in Applied Mathematics. Num Pages: 418 pages, biography. BIC Classification: PBW. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 235 x 164 x 31. Weight in Grams: 762. . 2007. 3rd. Hardcover. . . . . Books ship from the US and Ireland. Nº de ref. de la librería V9780387759333

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Descripción Springer-Verlag New York Inc., 2007. HRD. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería BB-9780387759333

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