Fictitious-domain method for the spectral problem for the Stokes operator
type: Item
instance of: scholarly article
zbMATH Open document ID: 0964.35117
author: M. Baizhumanov
author: Muhtarbay Otelbaev
author: Sh. S. Smagulov
publication date: 2001-06-10T00:00:00Z
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 1603338
zbMATH Keywords: Stokes equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: spectral problem
zbMATH Keywords: weak solution
zbMATH Keywords: fictitious domain
MaRDI profile type: Publication
title: Fictitious-domain method for the spectral problem for the Stokes operator
published in: Vychislitel'nye Tekhnologii
review text: The authors study the spectral problem for the Stokes operator on a domain in \(\mathbb R^3\) with smooth boundary. To solve the problem, the authors use the fictitious-domain method applied to an auxiliary problem in a suitable domain. The coefficients of the operator under consideration are extended by a small parameter \(\varepsilon\) in the so-called fictitious domain, and simultaneously some boundary value conditions are formed on the boundary of the domain.NEWLINENEWLINENEWLINEThe authors prove an existence theorem for the class of weak solutions to the auxiliary problem and establish a priori estimates for the solution obtained. As a result, this approach makes it possible to prove a convergence theorem and find the rate of convergence for eigenfunctions and eigenvalues to a solution of the original problem. This enables us to construct an iteration method for solving Navier--Stokes equations.
description: scientific article; zbMATH DE number 1603338