Numerical models for differential problems [electronic resource] / Alfio Quarteroni.
Quarteroni, Alfio, author.
2014
QA377 .Q83 2014eb
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Title Numerical models for differential problems [electronic resource] / Alfio Quarteroni.
Author Quarteroni, Alfio, author.
Uniform Title Modellistica numerica per problemi differenziali. English
Edition Second edition.
ISBN 9788847055223 electronic book
8847055229 electronic book
9788847055216
DOI https://doi.org/10.1007/978-88-470-5522-3
Published Milan ; New York: Springer, [2014]
Copyright ©2014
Language English
Description 1 online resource (xix, 656 pages) : illustrations.
Item Number 10.1007/978-88-470-5522-3 doi
Call Number QA377 .Q83 2014eb
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.
Note "Translated by Silvia Quarteroni from the original Italian edition: A. Quarteroni, Modellistica Numerica per Problemi Differenziali, 5th ed., Springer-Verlag Italia, Milano, 2012"-- t.p. verso.
Bibliography, etc. Note Includes bibliographical references (pages 635-648) and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Series MS&A (Series) ; v. 8.
Available in Other Form Numerical models for differential problems.
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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. 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.

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