A non-conforming domain decomposition for Raviart-Thomas vector fields in three dimensions

In this paper we are concerned with a domain decomposition method with non-matching grids for Raviart-Thomas finite elements. In this method, the normal complement of the resulting approximation is not continuous across the interface. To handle such non-conformity, a new matching condition will be introduced. Such matching condition still results in a symmetric and positive definite stiffness matrix. It will be shown that the approximate solution generated by the domain decomposition possesses the optimal energy error estimate.