An Iterative Substructuring Method for div-stable Finite Element Approximations of the Oseen Problem

Abstract

We apply an iterative substructuring algorithm with transmission conditions of Robin–Robin type to the discretized Oseen problem appearing as a linearized variant of the incompressible Navier–Stokes equations. Here we consider finite element approximations using velocity/pressure pairs which satisfy the Babuška–Brezzi stability condition. After proving well-posedness and strong convergence of the method, we derive an a-posteriori error estimate which controls convergence of the discrete subdomain solutions to the global discrete solution by measuring the jumps of the velocities at the interface. Additionally we obtain information how to design a parameter of the Robin interface condition which essentially influences the convergence speed. Numerical experiments confirm the theoretical results and the applicability of the method.