Numerical solutions of the thermistor problem by spline finite elements
type: Item
instance of: scholarly article
title: Numerical solutions of the thermistor problem by spline finite elements
zbMATH Open document ID: 1069.78007
published in: Applied Mathematics and Computation
publication date: 2005-02-22T00:00:00Z
review text: This paper deals with the numerical resolution of the following boundary value problem: \[ \begin{gathered} {\partial U\over\partial t}= {\partial^2U\over\partial t^2}+ \alpha\cdot\sigma\Biggl({\partial\phi\over\partial x}\Biggr)^2,\quad 0< x< 1,\quad t> 0,\\ {\partial\over\partial x} \Biggl(\sigma{\partial\phi\over\partial x}\Biggr)= 0,\quad 0< x< 1,\quad t> 0,\\ {\partial U\over\partial x}= 0,\quad x= 0,\quad t> 0,\\ {\partial U\over\partial x}+ \beta U= 0,\quad x= 1,\quad t> 0,\\ \phi(0, t)= 0,\quad t> 0,\\ \phi(1,t)= 1,\quad t> 0,\\ U(x,0)= 0,\quad 0\leq x\leq 1,\\ \phi(x,0)= x,\quad 0\leq x\leq 1,\end{gathered} \] where \[ \Phi(U)= \begin{cases} 1 & 0\leq u\leq 1\\ \delta & U> 1\end{cases} \] \[ \delta= 10^{-5},\quad \beta> 0, \] using a subdomain collocation and a Petrov-Galerkin method based on spline-finite elements. The resulting system of ordinary differential equations is solved by the usual Crank-Nicolson finite difference method using a variant of Thomas algorithm.
reviewed by: Agneta M. Balint
Mathematics Subject Classification ID: 78A55
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 78M25
zbMATH DE Number: 2136186
zbMATH Keywords: Thermistor
zbMATH Keywords: Step electrical conductivity
zbMATH Keywords: Subdomain collocation
zbMATH Keywords: Petrov-Galerkin method
author: S. Kutluay
author: A. Esen
MaRDI profile type: Publication
full work available at URL: j.amc.2003.12.125
OpenAlex ID: W2128560536
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DOI: 10.1016/J.AMC.2003.12.125
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description: scientific article; zbMATH DE number 2136186