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About this book
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas 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 encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math (AMS) series, which will focus on advanced textbooks ematical Sciences and research level monographs. Preface This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. One purpose of this book is to formalize basic tools that are commonly used by researchers in the field but never published. It is intended primarily for mathematics graduate students and mathematically sophisticated engineers and scientists. The book has been the basis for graduate-level courses at The Uni versity of Michigan, Penn State University and the University of Houston.
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Reviews
From the reviews of the 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. The book would work even better as a course text if computational and programming aspects of finite elements were to be integrated into the course work, or if a course on computational aspects of finite elements were offered in tandem."— ZENTRALBLATT MATH
"The authors have continued … the second edition, adding chapters on additive Schwarz preconditioners with applications to domain decomposition methods, and on a posteriori estimators and adaptivity. For researchers in finite elements and graduate students … this book is a valuable source, and provides an accessible route to the journal literature. … In summary, then, this is an excellent … introduction to key mathematical topics in the finite element method, and at the same time a valuable reference and source for workers in this area." (Batamanathan D. Reddy, Zentralblatt MATH, Vol. 1012, 2003)
"This book is devoted to the mathematical theory of finite element method and is the second edition of the book from 1994. … The book can be used as a basis for graduate-level courses for students in applied mathematics, physics, engineering sciences and other fields … . The numerous and interesting exercises round off and complete each chapter. … The book can be highly recommended to everyone who is teaching or researching in the field of numerical solution of partial differential equations." (I. P. Gavrilyuk, Zeitschrift für Analysis und ihre Anwendungen, Vol. 22 (1), 2003)
Authors and Affiliations
Bibliographic Information
Book Title: The Mathematical Theory of Finite Element Methods
Authors: Susanne C. Brenner, L. Ridgway Scott
Series Title: Texts in Applied Mathematics
DOI: https://doi.org/10.1007/978-1-4757-4338-8
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag New York 1994
eBook ISBN: 978-1-4757-4338-8Published: 17 April 2013
Series ISSN: 0939-2475
Series E-ISSN: 2196-9949
Edition Number: 1
Number of Pages: XII, 294
Topics: Numerical Analysis, Mathematical Methods in Physics, Numerical and Computational Physics, Simulation, Mathematical and Computational Engineering