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                <term xml:lang="en">Nonconforming finite elements</term>
                <term xml:lang="en">Robustness</term>
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              <p>In this paper, we consider triangular nonconforming finite element approximations of an interface elliptic problem. We propose two extensions of the conforming Nitsche's extended finite element method to the nonconforming case. The first one is obtained by adding stabilisation terms on the cut edges, and the second one by modifying the Crouzeix-Raviart basis functions on the cut cells. Both discrete problems are uniformly stable and yield optimal a priori error estimates, uniformly with respect to the diffusion parameters. Moreover, we show that they exhibit the same robustness with respect to the position of the interface as the classical conforming method. We then validate these results numerically. Finally, we propose a nonconforming approximation of the interface Stokes problem based on the modified Crouzeix-Raviart elements and we illustrate it numerically. c</p>
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              <p>Dans cet article, nous considérons les approximations par éléments finis triangulaires non conformes d'un problème elliptique d'interface. Nous proposons deux extensions de la méthode d'éléments finis étendue de Nitsche conforme au cas non conforme. La première est obtenue en ajoutant des termes de stabilisation sur les bords coupés, et la seconde en modifiant les fonctions de base de Crouzeix-Raviart sur les cellules coupées. Les deux problèmes discrets sont uniformément stables et donnent des estimations d'erreur a priori optimales, uniformément par rapport aux paramètres de diffusion. De plus, nous montrons qu'ils présentent la même robustesse vis-à-vis de la position de l'interface que la méthode classique de conformation. Nous validons ensuite ces résultats numériquement. Enfin, nous proposons une approximation non-conforme du problème de Stokes de l'interface basée sur les éléments de Crouzeix-Raviart modifiés et nous l'illustrons numériquement.</p>
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