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The Mathematical Theory of Finite Element Methods

  • Textbook
  • © 1994

Overview

Authors:
  1. Susanne C. Brenner

    1. Department of Mathematics, University of South Carolina, Columbia, USA

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    You can also search for this author in PubMed   Google Scholar

  2. L. Ridgway Scott

    1. Department of Mathematics, University of Houston, Houston, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Texts in Applied Mathematics (TAM, volume 15)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Basic Concepts

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 1-20

  3. Sobolev Spaces

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 21-45

  4. Variational Formulation of Elliptic Boundary Value Problems

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 47-66

  5. The Construction of a Finite Element Space

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 67-90

  6. Polynomial Approximation Theory in Sobolev Spaces

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 91-122

  7. n-Dimensional Variational Problems

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 123-148

  8. Finite Element Multigrid Methods

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 149-167

  9. Max-norm Estimates

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 169-193

  10. Variational Crimes

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 195-216

  11. Applications to Planar Elasticity

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 217-235

  12. Mixed Methods

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 237-260

  13. Iterative Techniques for Mixed Methods

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 261-276

  14. Applications of Operator-Interpolation Theory

    • Susanne C. Brenner, L. Ridgway Scott
    Pages 277-286

  15. Back Matter

    Pages 287-294
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Keywords

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.

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

  • Department of Mathematics, University of South Carolina, Columbia, USA

    Susanne C. Brenner

  • Department of Mathematics, University of Houston, Houston, USA

    L. Ridgway Scott

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