Finite element approximation to nonlinear coupled thermal problem
type: Item
instance of: scholarly article
title: Finite element approximation to nonlinear coupled thermal problem
zbMATH Open document ID: 1162.65055
author: Yanzhen Chang
author: Danping Yang
author: Jiang Zhu
published in: Journal of Computational and Applied Mathematics
publication date: 2009-03-17T00:00:00Z
review text: The authors study the nonlinear problem \[ \begin{aligned} &-\nabla (\mu(\;) \nabla u) =f,\text{ in }\Omega , \\ &-\Delta \theta =\mu (\theta) | \nabla u| ^2\text{ in }\Omega , \\ &u=0\;,\theta =0\text{ on }\partial \Omega , \end{aligned} \] which models problems with thermal effects. After establishing existence and regularity of the weak solution of the problem, they utilize the \(L^p\) theory for giving a convergence analysis of the standard finite element approximation in the general case where \(f\) is assumed only to be bounded. The authors also obtains optimal a priori error estimates in both \(W^{1,p}\)-norm and \(L^p\)-norm for the finite element approximations to the nonsingular solutions.
reviewed by: Adrian Carabineanu
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 5529469
zbMATH Keywords: nonlinear coupled system
zbMATH Keywords: nonsingular solution
zbMATH Keywords: finite element
zbMATH Keywords: error estimate
zbMATH Keywords: thermal effects
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.cam.2008.08.023
OpenAlex ID: W2008693008
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DOI: 10.1016/J.CAM.2008.08.023
description: scientific article; zbMATH DE number 5529469