
Numerical Models for Differential Problems
Alfio Quarteroni(Author)
Springer (Publisher)
2nd Edition
Published on 23. August 2016
Book
Paperback/Softback
XIX, 658 pages
978-88-470-5883-5 (ISBN)
Description
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
More details
Series
Edition
Softcover reprint of the original 2nd ed. 2014
Language
English
Place of publication
Milano
Italy
Illustrations
70 s/w Abbildungen, 93 farbige Abbildungen
XIX, 658 p. 163 illus., 93 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 37 mm
Weight
1013 gr
ISBN-13
978-88-470-5883-5 (9788847058835)
DOI
10.1007/978-88-470-5522-3
Schweitzer Classification
Other editions
Additional editions

Alfio Quarteroni
Numerical Models for Differential Problems
Book
12/2013
2nd Edition
Springer
€53.49
Article exhausted; check for reprint
Person
The Author is Professor and Director of the Chair of Modelling and Scientific Computing (CMCS) at the Institute of Analysis and Scientific Computing of EPFL, Lausanne (Switzerland), since 1998, Professor of Numerical Analysis at the Politecnico di Milano (Italy) since 1989, and Scientific Director of MOX, since 2002. Author of 22 books published with Springer, and of about 200 papers published in refereed international Journals, Conference Proceedings and Magazines, Alfio Quarteroni is actually one of the strongest and reliable mathematicians in the world in the field of Modelling and SC.
Content
1 A brief survey of partial differential equations.- 2 Elements of functional analysis.- 3 Elliptic equations.- 4 The Galerkin finite element method for elliptic problems.- 5 Parabolic equations.- 6 Generation of 1D and 2D grids.- 7 Algorithms for the solution of linear systems.- 8 Elements of finite element programming.- 9 The finite volume method.- 10 Spectral methods.- 11 Discontinuous element methods (DG and mortar).- 12 Diffusion-transport-reaction equations.- 13 Finite differences for hyperbolic equations.- 14 Finite elements and spectral methods for hyperbolic equations.- 15 Nonlinear hyperbolic problems.- 16 Navier-Stokes equations.- 17 Optimal control of partial differential equations.- 18 Domain decomposition methods.- 19 Reduced basis approximation for parametrized partial differential equations.