Estimation of the rate of convergence of difference schemes for the system of elasticity theory equations with discontinuous coefficients
type: Item
instance of: scholarly article
zbMATH Open document ID: 0983.65116
author: S. O. Vojtsekhivs'kyj
publication date: 2002-01-06T00:00:00Z
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 74B10
Mathematics Subject Classification ID: 74S20
zbMATH DE Number: 1685516
zbMATH Keywords: convergence
zbMATH Keywords: difference schemes
zbMATH Keywords: system of elasticity theory equations
zbMATH Keywords: discontinuous coefficients
zbMATH Keywords: Dirichlet problem
MaRDI profile type: Publication
title: Estimation of the rate of convergence of difference schemes for the system of elasticity theory equations with discontinuous coefficients
published in: Kraĭovi Zadachi dlya Dyferentsial'nykh Rivnyan'
review text: Let \(\Omega_0=\{x=(x_1,x_2):0<x_{\alpha}<l_{\alpha}\), \(\alpha=1,2\}\), let \(\Gamma_0\) be the boundary of \(\Omega_0\) and let the curve \(\Gamma\) divide the domain \(\Omega_0\) into subdomains \(\Omega_1, \Omega_2\), and \(\Gamma\in C^2\), \(\Gamma\cap\Gamma_0=\emptyset\). The author considers the Dirichlet problem for the system of elasticity theory equations with discontinuous coefficients NEWLINE\[NEWLINE-\sum_{\alpha,\beta=1}^{2}{\partial\over\partial x_{\alpha}} \Biggl(K_{\alpha\beta}(x){\partial\vec u\over\partial x_{\beta}}\Biggr)= \vec f(x),\quad x\in\Omega_0;\;\vec u(x)=0, x\in \Gamma_0,NEWLINE\]NEWLINE where \(\vec u(x)\) is the vector of elastic displacements, \(\vec f(x)\) is the vector of external forces, \(\vec f(x)\in L_2(\Omega_0)\); the matrices \(K_{\alpha\beta}(x), \alpha,\beta=1,2\) have some special form depending on the elasticity coefficients. The solution of the considered system satisfies the following conjunction conditions: \([\vec u]_{\Gamma}=0, [\sum_{\alpha,\beta=1}^{2}K_{\alpha\beta}{\partial\vec u\over\partial x_{\beta}}\cos(n,x_{\alpha})]_{\Gamma}=0\), where \(n\) is the external normal to \(\Gamma\); the symbol \([\varphi]_{\Gamma}\) means the jump of the function \(\varphi(x)\) on the curve \(\Gamma\). For the considered problem a difference scheme with accuracy order \(O(\sqrt{h})\) in the mesh norm \(W_2^1(\omega)\) is constructed.
reviewed by: Aleksandr D. Borisenko
description: scientific article; zbMATH DE number 1685516