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Published in:
01-05-2015
Finite Element Methods for the Temperature in Composite Media with Contact Resistance
Published in: Journal of Scientific Computing | Issue 2/2015
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Abstract
We consider a heat diffusion problem inside a composite medium. The contact resistance at the interface of constitutive materials allows for jumps of the temperature field. The transmission conditions need to be handled carefully and efficiently. The main concerns are accuracy and feasibility. Hybrid dual formulations are recommended here as the most popular mixed finite elements well adapted to account for the discontinuity of the temperature field. We therefore write the discretization of the heat problem by mixed finite elements and perform its numerical analysis. Of course, applying Lagrangian finite elements is possible in simple composite media but it turns out to be problematic for complex geometries. Nevertheless, we study the convergence of this finite element method to highlight some particularities related to the model under consideration and point out the effect of the contact resistance on the accuracy. Illustrative numerical experiments are finally provided to assess the theoretical findings.