A Finite Element Method Based on Weighted Interior Penalties for Heterogeneous Incompressible Flows

We propose a finite element scheme for the approximation of multidomain heterogeneous problems arising in the general framework of linear incompressible flows (e.g. Stokes' and Darcy's equations). We exploit stabilized mixed finite elements together with Nitsche type matching conditions that automatically adapt to the coupling of different subproblem combinations. Optimal error estimates are derived for the coupled problem. Then, we propose and analyze an iterative splitting strategy for the approximation of the multidomain solution by means of a sequence of independent and local subproblems. Thanks to the introduction of a suitable relaxation strategy,the iterative method turns out to be convergent for any possible coupling between subproblems.