The method of mothers for non-overlapping non-matching DDM

In this paper we introduce a variant of the three-field formulation where we use only two sets of variables. Considering, to fix the ideas, the Poisson equation with homogeneous Dirichlet boundary conditions in ?, our variables are i) the approximations uh of u in each sub-domain (each on its own grid), and ii) an approximation ?h of u on the skeleton (the union of the interfaces of the sub-domains) on an independent grid (that could often be uniform). The novelty is in the way to derive, from ?h, the values of the trace of uh on the boundary of each subdomain. We do it by solving an auxiliary problem on each subdomain boundary that resembles the mortar method but is more flexible. Under suitable assumptions, quasi-optimal error estimates are proved, uniformly with respect to the number and size of the subdomains. A preliminary version of the method and of its theoretical analysis has been presented in Bertoluzza et al. (15th international conference on domain decomposition methods, 2002).