Communications in Mathematical Sciences

Volume 16 (2018)

Number 7

Diffusion problems in multi-layer media with nonlinear interface contact resistance

Pages: 1849 – 1867

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n7.a5

Authors

Faker Ben Belgacem (Sorbonne Universités, Université de Technologie de Compiègne, Laboratoire de Mathématique Appliquée de Compiègne, France)

Faten Jelassi (Sorbonne Universités, Université de Technologie de Compiègne, Laboratoire de Mathématique Appliquée de Compiègne, France)

Maïmouna Mint Brahim (Sorbonne Universités, Université de Technologie de Compiègne, Laboratoire de Mathématique Appliquée de Compiègne, France)

Abstract

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, 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 code developers. We undertake the analysis of the non-linear heat problem for a large range of contact resistances and we investigate its discretization by hybrid dual finite element methods. Numerical experiments are presented at the end to support the theoretical results.

Keywords

thermal contact resistance, semi-linear problem, dual hybrid formulation, finite elements

2010 Mathematics Subject Classification

35J61, 80M10

Full Text (PDF format)

Received 31 July 2017

Accepted 14 June 2018

Published 7 March 2019