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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Numerical Approximation of Partial Differential Equations

Numerical Approximation of Partial Differential Equations

Valli, Alberto
Quarteroni, Alfio

Paperback

Series: Springer Computational Mathematics, Book 23

General Mathematics

ISBN10: 3540852670
ISBN13: 9783540852674
Publisher: Springer Nature
Published: Sep 24 2008
Pages: 544
Weight: 1.85
Height: 1.20 Width: 6.10 Depth: 9.30
Language: English
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).

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