Abstract
We develop a robust finite element method with domain decomposition for incompressible flows, allowing for control of the kinetic energy. First, we introduce a streamline upwind Petrov--Galerkin stabilization, which preserves the scaling of the Navier--Stokes equations and yields robustness with respect to the Péclet number. In view of parallelization, we then generalize the method in order to take into account several subdomains with independent finite element spaces, discontinuous at the interfaces. The interface conditions are treated by a generalized Nitsche-type method, also respecting the correct scaling. Detailed numerical experiments are presented in order to confirm robustness of the method and study its dependence on the different numerical parameters.
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