Convergence analysis for a second order Schwarz method for nonoverlapping subdomains

A second order Schwarz method for elliptic partial differential equations is developed and analyzed at a continuous level, which can be parallel implemented with local communications. It uses a second order boundary condition in terms of Poincaré-Steklov operators as its transmission condition on the interfaces. The convergence of the algorithm in H1 norm is obtained by using energy estimates, and convergence results hold on arbitrary geometry of subdomains with no cross points.