Convergence of the Neumann series in BEM for the Neumann problem of the Stokes system
type: Item
instance of: scholarly article
title: Convergence of the Neumann series in BEM for the Neumann problem of the Stokes system
zbMATH Open document ID: 1235.35221
author: Dagmar Medková
published in: Acta Applicandae Mathematicae
publication date: 2011-12-14T00:00:00Z
review text: The boundary value problem to the Stokes system is considered in a bounded domain \(\Omega\subset\mathbb{R}^m\) with connected Lipschitz boundary \(\Gamma\) \[ \begin{cases} \Delta u-\nabla p=0,\quad \text{div}\,u=0&\text{in}\;\Omega,\\ \mathbb{T}(u,p)n=g &\text{on}\;\partial\Omega=\Gamma. \end{cases} \] Here \(u\) is the velocity field, \(p\) is the pressure, \(\mathbb{T}(u,p)\) is the stress tensor, \[ \mathbb{T}(u,p)=[\nabla u +(\nabla u)^T]-pI, \] \(n\) is the unit outward normal on \(\Gamma\). The author formulates the condition to the vector \(g\) which is necessary and sufficient for the existence of a weak solution to the problem. The problem is reduced to the operator (integral) equation in the space \(H^{-1/2}(\Gamma)\). The solution of this equation might be found by successive approximations. The numerical realization of successive approximations is discussed in the paper.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 5988271
zbMATH Keywords: Stokes system
zbMATH Keywords: Neumann boundary condition
zbMATH Keywords: layer potentials
zbMATH Keywords: integral equations
zbMATH Keywords: successive approximations
reviewed by: Il'ya Sh. Mogilevskii
MaRDI profile type: Publication
full work available at URL: s10440-011-9643-5
OpenAlex ID: W2081148092
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DOI: 10.1007/S10440-011-9643-5
description: scientific article; zbMATH DE number 5988271