A Nonoverlapping Domain Decomposition Method For Nonconforming Finite Element Problems

A nonoverlapping domain decomposition method for nonconforming finite element problems of second order partial differential equations is developed and analyzed. In particular, its convergence is demonstrated and convergence rate is estimated. The method is based on a Robin boundary condition as its transmission condition together with a derivative-free transmission data updating technique on the interfaces. The method is directly presented to finite element problems without introducing any Lagrange multipliers. The method can be naturally applied to general multi-subdomain decompositions and implemented on parallel machines with local communications. The method also allows choosing subdomains very flexibly, which can be even as small as an individual element. Therefore, the method can be regarded as a bridge connecting between direct methods and iterative methods for linear systems. Finally, some numerical experiments are also presented to demonstrate the effectiveness of the method.