3D numerical simulation of an anisotropic bead type thermistor and multiplicity of solutions

We perform some 3D numerical experiments for the approximation of the solutions to a bead type thermistor problem. We consider the case of a diagonal anisotropic diffusion matrix whose jth entry is of the form |∂u/∂xj|pj−2∂u/∂xj, u being the temperature inside the thermistor and the exponents pj, 1≤...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics and computers in simulation Vol. 220; pp. 640 - 672
Main Authors: Lahrache, Manar, Ortegón Gallego, Francisco, Rhoudaf, Mohamed
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2024
Subjects:
Anisotropic Sobolev space
Finite element method
Non-uniformly elliptic system
Numerical solution
Thermistor problem
Thermistor problem
Finite element method
Non-uniformly elliptic system
Anisotropic Sobolev space
Numerical solution
ISSN:0378-4754, 1872-7166
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We perform some 3D numerical experiments for the approximation of the solutions to a bead type thermistor problem. We consider the case of a diagonal anisotropic diffusion matrix whose jth entry is of the form |∂u/∂xj|pj−2∂u/∂xj, u being the temperature inside the thermistor and the exponents pj, 1≤j≤3, lie in the interval (1,+∞). We first show some existence results for different notions of solutions, prove a maximum principle for each type of solution, and study certain symmetry properties for these solutions in a bead type thermistor. These properties lead us to the introduction of a symmetric solution and we show the existence of such a solution. We have developed a numerical algorithm for the computation of the numerical solutions in a bead type thermistor. This algorithm combines a fixed-point technique with a standard finite element method (FEM). Some numerical tests have shown the existence of non-symmetric solutions and this leads to multiple many solutions (at least three). We discuss the numerical results obtained for different values of the exponents pj and the applied voltage on different meshes.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2024.02.018