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 homogeneous Dirichlet problem for $$-\Delta\,u = g$$ in $$\Omega$$ , our variables are i) the approximations $$u_h^{s}$$ of u in each sub-domain $$\Omega^s$$ (each on its own grid), and ii) an approximation $$\Psi_h$$ 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 $$\Psi_h$$ , the values of each trace of $$u_h^{s}$$ on the boundary of each $$\Omega$$ . We do it by solving an auxiliary problem on each $$\partial\Omega^s$$ 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).