Numerical Approximation of Partial Differential Equations
This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic
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Alfio Quarteroni · Alberto Valli
Numerical Approximation of Partial Differential Equations With 59 Figures and 17 Tables
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Alfio Quarteroni École Polytechnique Fédérale de Lausanne Chaire de Modelisation et Calcul Scientifique (CMCS) Station 8 1015 Lausanne, Switzerland alfio.quarteroni@epfl.ch
Alberto Valli Università di Trento Dipartimento di Matematica Via Sommarive, 14 38050 Povo TN, Italy [email protected]
and MOX, Politecnico di Milano 20133 Milan, Italy
First softcover printing 2008
ISBN 978-3-540-85267-4
e-ISBN 978-3-540-85268-1
DOI 10.1007/978-3-540-85268-1 Springer Series in Computational Mathematics ISSN 0179-3632 Library of Congress Control Number: 97160884 Mathematics Subject Classification (1991): 65Mxx, 65Nxx, 65Dxx, 65Fxx, 35Jxx, 35Kxx, 35Lxx, 35Q30, 76Mxx © 2008, 1994 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Typesetting: by the authors using a Springer TEX macro package Printed on acid-free paper 98765 4321 springer.com
A Fulvia e Tiziana
Preface
Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation of partial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its v
