Encyclopedia of Computational Mechanics Second Edition, 6 Volume Set

0521432 - ÚGN 2020 RIV GB eng M - Část monografie knihy
Axelsson, Owe
Finite Difference Methods.
Encyclopedia of Computational Mechanics Second Edition, 6 Volume Set. Chichester: John Wiley & Sons, Ltd., 2017 - (Stein, E.; de Borst, R.; Hughes, T.), s. 1-52. ISBN 978-1-119-00379-3
Institucionální podpora: RVO:68145535
Klíčová slova: high order accuracy * monotone operators * maximum principle * extrapolation * stabilities * method of characteristics * graded meshes
Obor OECD: Applied mathematics

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.
Properties 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.
Difference 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.

Trvalý link: http://hdl.handle.net/11104/0306062