Study of a non-overlapping domain decomposition method: Poisson and Stokes problems. (Q1427206)

This works presents a theoretical analysis of an overlapping domain decomposition method previously introduced by \textit{J. L. Lions} and \textit{O. Pironneau} [C. R. Acad. Sci.,Paris, Sér. I, Math. 330, No.~10, 937--942 (2000; Zbl 0960.65102)]. It then proposes a variation of this method using a nonoverlapping decomposition of the domain and a penalty term on the interface. A convergence analysis is obtained for both the Poisson and the incompressible Stokes equations. Both theory and numerical results are given in the simplified case with only two subdomains and without a coarse space.