Numerical models for differential problems / Alfio Quarteroni.
Quarteroni, Alfio, author.
2017
QA377 .Q83 2017eb
Available Online

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Title Numerical models for differential problems / Alfio Quarteroni.
Author Quarteroni, Alfio, author.
Edition Third edition.
ISBN 9783319493169 (electronic book)
3319493167 (electronic book)
9783319493152
3319493159
DOI https://doi.org/10.1007/978-3-319-49316-9
Published Cham, Switzerland : Springer, 2017.
Language English
Description 1 online resource (xvii, 681 pages) : illustrations.
Other Standard Identifiers 10.1007/978-3-319-49316-9 doi
Call Number QA377 .Q83 2017eb
Dewey Decimal Classification 518/.64
Summary 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.-- Provided by publisher.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Digital File Characteristics text file PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed October 24, 2017).
Series MS&A (Series) ; v.16. 2037-5255
Available in Other Form Print version: 9783319493152
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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 Isogeometric analysis
12 Discontinuous element methods (D Gandmortar)
13 Diffusion-transport-reaction equations
14 Finite differences for hyperbolic equations
15 Finite elements and spectral methods for hyperbolic equations
16 Nonlinear hyperbolic problems
17 Navier-Stokes equations
18 Optimal control of partial differential equations
19 Domain decomposition methods
20 Reduced basis approximation for parametrized partial differential equations
References.

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