A smooth extension method for transmission problems

Astrid Decoene (1) , Sébastien Martin (1, 2) , Fabien Vergnet (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 LMO - Laboratoire de Mathématiques d'Orsay

In this work, we present a numerical method for the resolution of transmission problems with non-conformal meshes which preserves the optimal rates of convergence in space. The smooth extension method is a fictitious domain approach based on a control formulation stated as a minimization problem, that we prove to be equivalent to the initial transmission problem. Formulated as a minimization problem, the transmission problem can be solved with standard finite element function spaces and usual optimization algorithms. The method is applied to different transmission problems (Laplace, Stokes and a fluid-structure interaction problem) and compared to standard finite element methods.

Mots clés: transmission problem; interface problem; partial differential equations with discontinuous coefficients; fictitious domain; optimal rates of convergence; finite element method; smooth extension method

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Astrid Decoene, Sébastien Martin, Fabien Vergnet. A smooth extension method for transmission problems. 2019. ⟨hal-02146271v1⟩