Numerical Approximation of Partial Differential Equations

Alfio Quarteroni

ISBN 10: 3540852670 / ISBN 13: 9783540852674

Edité par Springer, Berlin, Springer Berlin Heidelberg, Springer, 2008

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 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 ofpartial 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 variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion). N° de réf. du vendeur 9783540852674

Détails bibliographiques

Titre : Numerical Approximation of Partial ...

Éditeur : Springer, Berlin, Springer Berlin Heidelberg, Springer

Date d'édition : 2008

Reliure : Taschenbuch

Etat : Neu

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Présentation de l'éditeur:

This soft cover reprint of the popular hardbound thoroughly illustrates numerical methods. It carries out their stability and convergence analysis, derives error bounds, and discusses the algorithmic aspects relative to their implementation.