Effect of errors in the spatial geometry for temperature dependent Stokes flow
type: Item
instance of: scholarly article
title: Effect of errors in the spatial geometry for temperature dependent Stokes flow
zbMATH Open document ID: 0935.76020
DOI: 10.1016/S0021-7824(99)00011-2
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2000-04-26T00:00:00Z
review text: The coupled Stokes and heat conduction equations \(\frac{\partial u_{i}}{\partial t}= -\frac{\partial p}{\partial x_{i}}+\Delta u_{i}+g_{i}T\), \(\frac{\partial u_{i}}{\partial x_{i}}=0\), \(\frac{\partial T}{ \partial t}+u_{i}\frac{\partial T}{\partial x_{i}}= \Delta T\) are considered with appropriate initial and boundary conditions. The authors study the continuous dependence of solution on spatial geometry, and derive an error estimate for the difference between the exact solution to the true physical problem \(( u,T,p)\) and the exact solution on an approximate domain. The derivation involves the introduction of various auxiliary problems and estimates in \(L^{p}\) for related functions.
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 1344453
zbMATH Keywords: Stokes flow
zbMATH Keywords: approximate domain
zbMATH Keywords: heat equation
zbMATH Keywords: \(L(p)\)-estimate
zbMATH Keywords: error estimate
author: L. E. Payne
author: Brian Straughan
reviewed by: Vladimir Mityushev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1344453