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Series : APPLIED MATHEMATICAL SCIENCES

Least-Squares Finite Element Methods

Least-Squares Finite Element Methods
Author
Bochev, Pavel B./ Gunzburger, Max D. 
Publisher
Springer-Verlag 
Publication Date
Mar, 2009 
ISBN
0387308881 or 9780387308883
HARDCOVER 
660 Pages
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¥ 15,707 (tax included)

Description

This book offers a thorough and systematic examination of theoretical and computational aspects of least-squares finite element methods. The range of topics spans formal mathematical analysis and framework for least squares methods, application of this framework to concrete partial differential equations and discussion of the computational properties of the methods. The abstract least-squares framework will help readers navigate the realm of least-squares methods while the many numerical examples provide a valuable practical guide to these methods. Most of the necessary background material is contained in several appendices. Chapter summaries and detailed illustrations are included . Graduate students and computational science researchers will find this book useful.

Contents

Part I. Survey of Variational Principles and Associated Finite Element Methods.
Classical Variational Methods.
Alternative Variational Formulations.

Part II. Abstract Theory of Least-Squares Finite Element Methods.
Mathematical Foundations.
First-Order Agmon-Douglis-Nirenberg Systems.

Part III. Least-Squares Methods for Elliptic Problems.
Basic First-Order Systems.
Application to Key Elliptic Problems.

Part IV. Extensions of Least-Squares Methods to other Problems.
The Navier-Stokes Equations.
Dissipative Time Dependent Problems.
Hyperbolic Problems.
Control and optimization Problems.
Other Topics.

Part V. Supplementary Material.
A. Analysis Tools.
B. Finite Element Spaces.
C. Discrete Norms and Operators.
D. The Complementing Condition.

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