Steady-state solution of the PTC thermistor problem using a quadratic spline finite element method
type: Item
instance of: scholarly article
title: Steady-state solution of the PTC thermistor problem using a quadratic spline finite element method
zbMATH Open document ID: 1050.80003
DOI: 10.1080/10241230212911
author: Yanyan Li
published in: Mathematical Problems in Engineering
publication date: 2004-09-07T00:00:00Z
full work available at URL: https://eudml.org/doc/51053
review text: This paper deals with a dimensionless mathematical model of the PCT thermistor: \[ u_t=u_{xx}+\gamma\sigma(u)|\phi_x|^2, \;0<x<1, \;t>0 \] subject to the conditions \(u_x=0\) for \(x=0\), \(t>0\), \(u_x+\beta u=0\) for \(x=1\), \(t>0\), \(u(x,0)=0\) for \(0\leq x\leq 1\), where \(u\) is the temperature and \(\phi\) is the electrical potential. A finite element solution is constructed using quadratic spatial elements and finite difference approximation in time. The numerical and analytical steady-state solution of the problem is covered.
Mathematics Subject Classification ID: 80M10
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 65M60
zbMATH DE Number: 2097941
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
OpenAlex ID: W2082433657
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description: scientific article; zbMATH DE number 2097941