Numerical Approximation of Partial Differential Equations by Alfio Quarteroni

Numerical Approximation of Partial Differential Equations by Alfio Quarteroni

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).

"..The book is excellent and is addressed to post-graduate students, research workers in applied sciences as well as to specialists in numerical mathematics solving PDE. Since it is written very clearly, it would be acceptable for undergraduate students in advanced courses of numerical mathematics. Readers will find this book to be a great pleasure."--MATHEMATICAL REVIEWS

Since more than ten years the authors have performed researches in the field of numerical approximation of partial differential equations, especially the finite element approximation of problems in electromagnetics. They have published many papers on numerical approximation of partial differential equations on some of the most important journal devoted to this topic. The second author has written two other books on the subject: A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, Springer, 1997 (second edition); A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations, Oxford University Press, 1999

SKU	Unavailable
ISBN 13	9783540852674
ISBN 10	3540852670
Title	Numerical Approximation of Partial Differential Equations
Author	Alfio Quarteroni
Series	Springer Series In Computational Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer
Year published	2008-09-24
Number of pages	544
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.