Finite Difference Methods

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F17%3A00521432" target="_blank" >RIV/68145535:_____/17:00521432 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1002/9781119176817.ecm2002" target="_blank" >http://dx.doi.org/10.1002/9781119176817.ecm2002</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/9781119176817.ecm2002" target="_blank" >10.1002/9781119176817.ecm2002</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Finite Difference Methods

Popis výsledku v původním jazyce

It is shown how difference methods lead to monotone operators with uniformly bounded inverses for which discretization error estimates for the solution and its derivatives can readily be derived. Higher order of accuracy can be achieved for sufficiently regular solutions by extrapolation or by the use of various higher order difference methods.nProperties of solutions of elliptic, parabolic, hyperbolic, and convection‐dominated convection–diffusion problems as well as positivity and continuous and discrete maximum principles of the solution are shown. Computational aspects of solving difference equations are discussed. Stable discretization of time‐dependent problems is shown for parabolic problems and hyperbolic problems of first and second order. Various discretization methods for convection‐dominated convection–diffusion problems, including method of characteristics, are presented.nDifference methods have their main advantages in that regular meshes can be used. To handle more general problems, adaptive mesh refinement and use of graded meshes are discussed. Use of local Green's functions and other examples of exact difference schemes are also presented.n

Název v anglickém jazyce

Finite Difference Methods

Popis výsledku anglicky

It is shown how difference methods lead to monotone operators with uniformly bounded inverses for which discretization error estimates for the solution and its derivatives can readily be derived. Higher order of accuracy can be achieved for sufficiently regular solutions by extrapolation or by the use of various higher order difference methods.nProperties of solutions of elliptic, parabolic, hyperbolic, and convection‐dominated convection–diffusion problems as well as positivity and continuous and discrete maximum principles of the solution are shown. Computational aspects of solving difference equations are discussed. Stable discretization of time‐dependent problems is shown for parabolic problems and hyperbolic problems of first and second order. Various discretization methods for convection‐dominated convection–diffusion problems, including method of characteristics, are presented.nDifference methods have their main advantages in that regular meshes can be used. To handle more general problems, adaptive mesh refinement and use of graded meshes are discussed. Use of local Green's functions and other examples of exact difference schemes are also presented.n

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Encyclopedia of Computational Mechanics Second Edition, 6 Volume Set

ISBN

978-1-119-00379-3

Počet stran výsledku

52

Strana od-do

1-52

Počet stran knihy

4024

Název nakladatele

John Wiley & Sons, Ltd.

Místo vydání

Chichester

Kód UT WoS kapitoly

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