A variational finite element method for the two-dimensional Stokes problem
type: Item
instance of: scholarly article
title: A variational finite element method for the two-dimensional Stokes problem
zbMATH Open document ID: 0845.76050
DOI: 10.1016/0045-7825(93)90003-G
author: Yanyan Li
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1996-05-06T00:00:00Z
review text: In two dimensions, the steady Stokes problem in stream function-vorticity variables is reduced to a Dirichlet problem for the biharmonic operator. A new formulation for the decomposition of the biharmonic operator using the potential theory is presented. The problem comes down to the calculation of a function defined on the boundary, which is the solution of a variational problem. The first part of the paper is devoted to the analysis of the continuous problem, and the variational formulation on the boundary is studied. By using a suitable finite element approximation, similar properties for the discrete problem are found. These properties imply that the discrete function is the solution of a linear system, whose matrix is full, but symmetric and positive-definite. Among the iterative methods, we use the conjugate gradient method, which seems suitable in the context. Numerical results concerning the problem of steady flow in a square cavity are presented.
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76M30
Mathematics Subject Classification ID: 76D07
zbMATH DE Number: 873988
zbMATH Keywords: stream function-vorticity variables
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: biharmonic operator
zbMATH Keywords: potential theory
zbMATH Keywords: continuous problem
zbMATH Keywords: discrete problem
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: square cavity
MaRDI profile type: Publication
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full work available at URL: 0045-7825(93)90003-g
OpenAlex ID: W1982305401
description: scientific article; zbMATH DE number 873988