Numerical Analysis of a Stable Finite Volume Scheme for a Generalized Thermistor Model-Reference-Cited by-同舟云学术

Numerical Analysis of a Stable Finite Volume Scheme for a Generalized Thermistor Model

Published:2020-07-16 Issue:1 Volume:21 Page:69-87
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Ghilani Mustapha¹,Quenjel El Houssaine²,Rhoudaf Mohamed³

Affiliation:

1. Moulay Ismaïl University , ENSAM-Meknès, B.P. 15290 EL Mansour 50 500 Meknès , Morocco

2. Côte d’Azur University , LJAD, CNRS UMR 7351, and COFFEE team, INRIA Sophia Antipolis Méediterranée, Parc Valrose 06108 Nice Cedex 02 , France

3. Moulay Ismaïl University , Faculty of Sciences, B.P. 11201 Zitoune 50 500 Meknès , Morocco

Abstract

Abstract A generalized thermistor model is discretized thanks to a fully implicit vertex-centered finite volume scheme on simplicial meshes. An assumption on the stiffness coefficients is mandatory to prove a discrete maximum principle on the electric potential. This property is fundamental to handle the stability issues related to the Joule heating term. Then the convergence to a weak solution is established. Finally, numerical results are presented to show the efficiency of the methodology and to illustrate the behavior of the temperature together with the electric potential within the medium.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Reference40 articles.

1. M. Afif and B. Amaziane, Convergence of finite volume schemes for a degenerate convection–diffusion equation arising in flow in porous media, Comput. Methods Appl. Mech. Engrg. 191 (2002), no. 46, 5265–5286.

2. G. Akrivis and S. Larsson, Linearly implicit finite element methods for the time-dependent Joule heating problem, BIT 45 (2005), no. 3, 429–442.

3. W. Allegretto, Y. Liu and A. Zhou, A box scheme for coupled systems resulting from microsensor thermistor problems, Dyn. Contin. Discrete Impuls. Syst. 5 (1999), no. 1–4, 209–223.

4. W. Allegretto and H. Xie, Existence of solutions for the time-dependent thermistor equations, IMA J. Appl. Math. 48 (1992), no. 3, 271–281.

5. B. Andreianov, M. Bendahmane and K. H. Karlsen, Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations, J. Hyperbolic Differ. Equ. 7 (2010), no. 01, 1–67.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Discrete duality finite volume scheme for a generalized Joule heating problem;Calcolo;2024-02-07

2. On Numerical Approximation of Diffusion Problems Governed by Variable-Exponent Nonlinear Elliptic Operators;Vietnam Journal of Mathematics;2022-10-24

3. CAPACITY SOLUTION AND NUMERICAL APPROXIMATION TO A NONLINEAR COUPLED ELLIPTIC SYSTEM IN ANISOTROPIC SOBOLEV SPACES;Journal of Applied Analysis & Computation;2022