DOMAIN DECOMPOSITION BY A COUPLING OF CONFORMING AND EQUILIBRIUM FINITE-ELEMENTS

A non-standard finite element method, solving elliptic problems, is presented. This method is based on a non overlapping decomposition of the whole domain OMEGA; subdomains, OMEGA1 and OMEGA2, are not necessarly connected, and could depend on a OMEGA-triangulation. A conforming variational formulation of the initial problem is used on OMEGA1, whereas an equilibrium formulation is established on OMEGA2. A coupled equations system in which all matching conditions remain implicit is hereby obtained. Existence and uniqueness of the approximated problems solution are given and the method convergence rate (according to convenient norm) is specified.