@misc{10498/32742,
year = {2024},
month = {2},
url = {http://hdl.handle.net/10498/32742},
abstract = {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
𝑗�th entry is of the form|𝜕�𝑢�∕𝜕�𝑥�𝑗�|𝑝�𝑗�−2𝜕�𝑢�∕𝜕�𝑥�𝑗�,𝑢� being the temperature inside the thermistor and
the exponents 𝑝�𝑗�,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 𝑝�𝑗� and the applied voltage on different
meshes.},
publisher = {Elservier},
keywords = {Thermistor problem},
keywords = {Anisotropic Sobolev space},
keywords = {Non-uniformly elliptic system},
keywords = {Finite element method},
keywords = {Numerical solution},
title = {3D numerical simulation of an anisotropic bead type thermistor and multiplicity of solutions},
doi = {10.1016/j.matcom.2024.02.018},
author = {Lahrache, Manar and Ortegón Gallego, Francisco and Rhoudaf, Mohamed},
}