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Texts in Applied Mathematics 15: The Mathematical Theory of Finite Element Methods, Third Edition (Hardback)
Texts in Applied Mathematics 15: The Mathematical Theory of Finite Element Methods, Third Edition (Hardback)
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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 Poincaré-Freidrichs inequalities for piecewise W1p functions. New exercises have also been added throughout.
"The initial chapter provides an introduction 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."
BRIEF CONTENTS
- Series Preface
- Preface to the Third Edition
- Preface to the Second Edition
- Preface to the First Edition
- 0 - Basic Concepts
- 1 - Sobolev Spaces
- 2 - Variational Formulation of Elliptic Boundary Value Problems
- 3 - The Construction of a Finite Element Space
- 4 - Polynomial Approximation Theory in Sobolev Spaces
- 5 - n-Dimensional Variational Problems
- 6 - Finite Element Multigrid Methods
- 7 - Additive Schwarz Preconditioners
- 8 - Max-norm Estimates
- 9 - Adaptive Meshes
- 10 - Variational Crimes
- 11 - Applications to Planar Elasticity
- 12 - Mixed Methods
- 13 - Iterative Techniques for Mixed Methods
- 14 - Applications of Operator-Interpolation Theory
- References
- Index
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PUBLISHER: Springer Science+Business Media
ISBN-13: 9780387759333
ISBN-10: 0387759336