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≤...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematics and computers in simulation Jg. 220; S. 640 - 672
Hauptverfasser: Lahrache, Manar, Ortegón Gallego, Francisco, Rhoudaf, Mohamed
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.06.2024
Schlagworte:
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-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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