The Lagrange-Euler method for the numerical solution of multidimensional problems of convective diffusion.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1078.80508
author: V. F. Demchenko
author: O. B. Lisnyj
publication date: 2001-11-04T00:00:00Z
Mathematics Subject Classification ID: 80M20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 74R20
zbMATH DE Number: 1668356
zbMATH Keywords: convective diffusion
zbMATH Keywords: numerical scheme
zbMATH Keywords: combined method
zbMATH Keywords: uniform convergence
MaRDI profile type: Publication
title: The Lagrange-Euler method for the numerical solution of multidimensional problems of convective diffusion.
published in: Dopovidi Natsional'noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky
review text: As a sample problem, the first boundary-value problem for the equation of convective diffusion in a rectangle is considered. Advantages and disadvantages of known numerical schemes of solution are discussed. For the approximation of equations of convective transport, the combined Lagrange-Euler method is suggested. Details of grid formation and derivatives approximation are explained. The error introduced by the numerical scheme is investigated. A theorem that the suggested scheme is uniformly converging when both temporal and spatial steps of discretization independently tend to zero and that this scheme has first order accuracy is proved. Comparison of a test example with the analytic solution for an infinite domain is done. Isolines of mean-square error are presented.
description: scientific article; zbMATH DE number 1668356