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 -triangle 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(s). We do it by solving an auxiliary problem on each partial derivative 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).