Numerical Approximation of Partial Differe...

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Beschreibung

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).

Inhaltsverzeichnis

Basic Concepts and Methods for PDEs' Approximation.- Numerical Solution of Linear Systems.- Finite Element Approximation.- Polynomial Approximation.- Galerkin, Collocation and Other Methods.- Approximation of Boundary Value Problems.- Elliptic Problems: Approximation by Galerkin and Collocation Methods.- Elliptic Problems: Approximation by Mixed and Hybrid Methods.- Steady Advection-Diffusion Problems.- The Stokes Problem.- The Steady Navier-Stokes Problem.- Approximation of Initial-Boundary Value Problems.- Parabolic Problems.- Unsteady Advection-Diffusion Problems.- The Unsteady Navier-Stokes Problem.- Hyperbolic Problems.

Erscheinungsjahr:	2008
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xvi 544 S.
ISBN-13:	9783540852674
ISBN-10:	3540852670
Sprache:	Englisch
Herstellernummer:	978-3-540-85267-4
Autor:	Quarteroni, Alfio Valli, Alberto
Hersteller:	Springer Springer, Berlin Springer Berlin Heidelberg
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Abbildungen:	XVI, 544 p. 59 illus.
Maße:	30 x 155 x 235 mm
Von/Mit:	Alfio Quarteroni (u. a.)
Erscheinungsdatum:	24.09.2008
Gewicht:	0,854 kg

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