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In this paper, we study the stability of the non symmetric version of theNitsche's method without penalty for domain decomposition. The Poisson problemis considered as a model problem. The computational domain is divided into twosubdomain that can have different material parameters. In the first half of thepaper we are interested in nonconforming domain decomposition, each subdomainis meshed independently of each other. In the second half, we study unfitteddomain decomposition, the computational domain has only one mesh and we allowthe interface to cut elements of the mesh. The fictitious domain method is usedto handle this specificity. We prove $H^1$-convergence and $L^2$-convergence ofthe error in both cases. Some numerical results are provided to corroborate thetheoretical study.

Fitted and unfitted domain decomposition using penalty free Nitsche method for the Poisson problem with discontinuous material parameters