A nonoverlapping domain decomposition method for stabilized finite element approximations of the Oseen equations

A nonoverlapping domain decomposition algorithm of Robin–Robin type is applied to the discretized Oseen equations using stabilized finite element approximations of velocity and pressure thus allowing in particular equal-order interpolation. As a crucial result we have to inspect the proof of a modified inf–sup condition, in particular, the dependence of the stability constant with respect to the Reynolds number (cf. appendix). After proving coercivity and strong convergence of the method, we derive an a posteriori estimate which controls convergence of the discrete subdomain solutions to the global discrete solution provided that jumps of the discrete solution converge at the interface. Furthermore, we obtain information on the design of some free parameters within the Robin-type interface condition which essentially influence the convergence speed. Some numerical results confirm the theoretical ones.