An iteration method for the mixed formulation of parameter dependent problems related to the Stokes equations
type: Item
instance of: scholarly article
title: An iteration method for the mixed formulation of parameter dependent problems related to the Stokes equations
zbMATH Open document ID: 0628.76039
DOI: 10.1007/BF00277698
published in: Computational Mechanics
publication date: 1986-01-01T00:00:00Z
review text: As a generalization of the Stokes equations, the following problem is considered: given \(\{\) f,g\(\}\in V\times W\) and \(\epsilon\geq 0\), find \(\{u_{\epsilon},\lambda_{\epsilon}\}\in V\times W\) such that \(Au_{\epsilon}+B^*\lambda_{\epsilon}=f,\) \(Bu_{\epsilon}-\epsilon \lambda_{\epsilon}=g,\) where V and W are real Hilbert spaces, A, B and \(B^*\) are linear bounded operators, \(B^*\) being the adjoint of B, A being non-negative. To investigate the problem, an iteration scheme is used with a theorem on its convergence, the penalty method being used as the basic one. Also, a case is considered when A is symmetric. All the obtained results are shown to be applicable to the finite-element method.
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 4022872
zbMATH Keywords: Stokes equations
zbMATH Keywords: real Hilbert spaces
zbMATH Keywords: finite-element method
author: Fumio Kikuchi
author: Milagros P. Navarro
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4022872