Diffusion Problems in Multi-layer Media with Nonlinear Interface Contact Resistance

F Ben Belgacem (1) , Faten Jelassi (2) , Maimouna Mint Brahim (3)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne
2 ENIT - Ecole Nationale d'Ingénieurs de Tunis
3 I2M - Institut de Mécanique et d'Ingénierie de Bordeaux

The purpose is a finite element approximation of the heat diffusion problem in composite media, with non-linear contact resistance at the interfaces. As already explained in [Journal of Scientific Computing, {\bf 63}, 478-501(2015)], hybrid dual formulations are well fitted to complicated composite geometries and provide tractable approaches to variationally express the jumps of the temperature. The finite elements spaces are standard. Interface contributions are added to the variational problem to account for the contact resistance. This is an important advantage for computing codes developers. We undertake the analysis of the non-linear heat problem for a large range of contact resistance and we investigate its discretization by hybrid dual finite element methods. Numerical experiments are presented at the end to support the theoretical results.

Domaines: Analyse numérique [math.NA]

F Ben Belgacem, Faten Jelassi, Maimouna Mint Brahim. Diffusion Problems in Multi-layer Media with Nonlinear Interface Contact Resistance. 2017. ⟨hal-01800481v1⟩