Numerical approximation of partial differential equations

Alfio Quarteroni, Alberto Valli (auth.)3540852670, 9783540852674

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 aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is one of its main features. Many kinds of problems are addressed. A comprehensive theory of Galerkin method and its variants, as well as that of collocation methods, are developed for the spatial discretization. These theories are then specified to two numerical subspace realizations of remarkable interest: the finite element method and the spectral method.

From the reviews:

“…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

Table of contents :
Front Matter….Pages I-XVI
Introduction….Pages 1-16
Numerical Solution of Linear Systems….Pages 17-71
Finite Element Approximation….Pages 73-100
Polynomial Approximation….Pages 101-127
Galerkin, Collocation and Other Methods….Pages 129-157
Elliptic Problems: Approximation by Galerkin and Collocation Methods….Pages 159-216
Elliptic Problems: Approximation by Mixed and Hybrid Methods….Pages 217-255
Steady Advection-Diffusion Problems….Pages 257-296
The Stokes Problem….Pages 297-337
The Steady Navier-Stokes Problem….Pages 339-362
Parabolic Problems….Pages 363-404
Unsteady Advection-Diffusion Problems….Pages 405-427
The Unsteady Navier-Stokes Problem….Pages 429-448
Hyperbolic Problems….Pages 449-508
Back Matter….Pages 509-543