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In this work a Nitsche-based imposition of generalized Navier conditions oncut meshes for the Oseen problem is presented. Other methods from literaturedealing with the generalized Navier condition impose this condition by means ofsubstituting the tangential Robin condition in a classical Galerkin way. Thesemethods work fine for a large slip length coefficient but lead to conditioningand stability issues when it approaches zero. We introduce a novel method forthe weak imposition of the generalized Navier condition which remainswell-posed and stable for arbitrary choice of slip length, including zero. Themethod proposed here builds on the formulation done by [1]. They impose a Robincondition for the Poisson problem by means of Nitsche's method for an arbitrarycombination of the Dirichlet and Neumann parts of the condition. The analysisconducted for the proposed method is done in a similar fashion as in [2], butis done here for a more general type of boundary condition. The analysis provesstability for all flow regimes and all choices of slip lengths. Also anL2-optimal estimate for the velocity error is shown, which was not conducted inthe previously mentioned work. A numerical example is carried out for varyingslip lengths to verify the robustness and stability of the method with respectto the choice of slip length. Even though proofs and formulations are presentedfor the more general case of an unfitted grid method, they can easily bereduced to the simpler case of a boundary-fitted grid with the removal of theghost-penalty stabilization terms.

A Nitsche cut finite element method for the Oseen problem with general Navier boundary conditions