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Synopsis
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 andisoparametric 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 keymathematical topics in the finite element method, and at the same time a valuable reference and source for workers in the area."
(Zentralblatt, 2002)
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The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics, 15)
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The Mathematical Theory of Finite Element Methods (Paperback)
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Springer-Verlag New York Inc., New York, NY, 2010
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Paperback. Condition: new. Paperback. Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAMwillpublishtextbookssuitableforuseinadvancedundergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich College Park, Maryland S.S. Antman Preface to the Third Edition This edition contains four new sections on the following topics: the BDDC domain decomposition preconditioner (Section 7.8), a convergent ad- tive algorithm (Section 9.5), interior penalty methods (Section 10.5) and 1 Poincar e-Friedrichs inequalities for piecewise W functions (Section 10.6). Antman Preface to the Third Edition This edition contains four new sections on the following topics: the BDDC domain decomposition preconditioner (Section 7.8), a convergent ad- tive algorithm (Section 9.5), interior penalty methods (Section 10.5) and 1 Poincar e-Friedrichs inequalities for piecewise W functions (Section 10.6). Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781441926111
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Paperback. Condition: Very Good. A copy that has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged. This is the third and yet further updated edition of a highly regarded math ematical 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 resea rchers in the field but not previously published. The book is ideal for mat hematicians as well as engineers and physical scientists. It can be used fo r a course that provides an introduction to basic functional analysis, appr oximation 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. Editorial Reviews 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 st udents who have taken the trouble to master at least some of the advanced m aterial 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 acc. Seller Inventory # RWARE0000062216
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