Least-Squares Finite Element Methods / Edition 1

by Pavel B. Bochev, Max D. Gunzburger

Overview

Since their emergence in the early 1950s,finite element methods have become one of the most versatile and powerful methodologies for the approximate numerical solution of partial differential equations. At the time of their inception,finite e- ment methods were viewed primarily as a tool for solving problems in structural analysis. However, it did not take long to discover thatfinite element methods could be applied with equal success to problems in other engineering and scientific fields. Today,finite element methods are also in common use, and indeed are often the method of choice, for incompressible—fluid flow, heat transfer, electromagnetics, and advection-diffusion-reaction problems, just to name a few. Given the early conn- tion betweenfinite element methods and problems engendered by energy minimi- tion principles, it is not surprising that the first mathematical analyses offinite e- ment methods were given in the environment of the classical Rayleigh–Ritz setting. Yet again, using the fertile soil provided by functional analysis in Hilbert spaces, it did not take long for the rigorous analysis offinite element methods to be extended to many other settings. Today,finite element methods are unsurpassed with respect to their level of theoretical maturity.

Product Details

ISBN-13:	9780387308883
Publisher:	Springer New York
Publication date:	03/23/2009
Series:	Applied Mathematical Sciences , #166
Edition description:	2009
Pages:	660
Product dimensions:	6.30(w) x 9.30(h) x 1.70(d)

Table of Contents

Survey of Variational Principles and Associated Finite Element Methods..- Classical Variational Methods.- Alternative Variational Formulations.- Abstract Theory of Least-Squares Finite Element Methods.- Mathematical Foundations of Least-Squares Finite Element Methods.- The Agmon#x2013;Douglis#x2013;Nirenberg Setting for Least-Squares Finite Element Methods.- Least-Squares Finite Element Methods for Elliptic Problems.- Scalar Elliptic Equations.- Vector Elliptic Equations.- The Stokes Equations.- Least-Squares Finite Element Methods for Other Settings.- The Navier#x2013;Stokes Equations.- Parabolic Partial Differential Equations.- Hyperbolic Partial Differential Equations.- Control and Optimization Problems.- Variations on Least-Squares Finite Element Methods.- Supplementary Material.- Analysis Tools.- Compatible Finite Element Spaces.- Linear Operator Equations in Hilbert Spaces.- The Agmon#x2013;Douglis#x2013;Nirenberg Theory and Verifying its Assumptions.

Editorial Reviews

From the reviews: “In the book under review, the authors give a unified and comprehensive treatment of least-squares finite element methods and discuss important implementation issues that are critical to their success in practice. … This book is valuable both for researchers and practitioners working in least-squares finite element methods. … In addition, others will find it a great reference for learning about the theory and implementation of the least-squares finite element methods.” (Tsu-Fen Chen, Mathematical Reviews, Issue 2010 b)

From the Publisher