Non-overlapping Domain Decomposition Method for a Nodal Finite Element Method

A new approach is proposed to deal with degrees of freedom shared by more than two subdomains in the context of a non-overlapping domain decomposition procedure for solving a system related to a nodal finite element method. The main feature of the method is to preserve the continuity requirements on the unknowns and the finite element equations at these degrees of freedom. We prove that the corresponding algorithm can be seen as a converging iterative method to solve the finite element system and that it cannot break down. Each iteration is obtained by solving uncoupled finite element systems posed in each subdomain and, in contrast to a strict domain decomposition method, is completed by solving a linear system whose unknowns are the above special degrees of freedom.