This paper investigates the propagation of a flame front in a periodic heterogeneous solid medium under the effect of temperature. The system of PDEs for the temperature and the interface form a free boundary system composed of a parabolic equation coupled with a Hamilton-Jacobi type equation. We propose a monotonous and stable numerical scheme and verify numerically that the numerical solution converges to a traveling wave solution for large time.

free boundary problem, heterogeneous medium, traveling wave solution, system of parabolic/Hamilton-Jacobi equations, numerical resolution, finite element.

Received: November 6, 2024; Revised: December 20, 2024; Accepted: December 25, 2024; Published: January 20, 2025

How to cite this article: Mohamed KARIMOU GAZIBO and Aboubacar ABDOU, Numerical resolution of a free boundary problem in a heterogeneous medium, International Journal of Numerical Methods and Applications 25(1) (2025), 151-186. https://doi.org/10.17654/0975045225007

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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