The accuracy of approximations on rectangular grids in problems of the theory of elasticity with singularities
type: Item
instance of: scholarly article
title: The accuracy of approximations on rectangular grids in problems of the theory of elasticity with singularities
zbMATH Open document ID: 0833.73071
author: I. G. Belukhina
published in: Computational Mathematics and Mathematical Physics
publication date: 1996-03-24T00:00:00Z
review text: The asymptotic accuracy of a two-parameter family of difference schemes (including the finite-element method scheme with bilinear elements), which approximate mixed boundary-value problems on a regular rectangular grid in a half-plane for a system of equations of the linear theory of elasticity in which the first derivatives of the solutions have a singularity \(O (r^{- 1/2})\), is investigated. Integral representations of the grid solutions are found and their asymptotic series at infinity are obtained. The principal term of the error, of size \(O (h/r^{1/2})\), where \(r\) is the distance from the point where the type of boundary conditions changes, is computed.
Mathematics Subject Classification ID: 74S20
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 74B05
zbMATH DE Number: 826009
zbMATH Keywords: integral representations
zbMATH Keywords: two-parameter family of difference schemes
zbMATH Keywords: asymptotic series at infinity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 826009