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 −∆ u = g in Ω, our variables are i) the approximations of u in each sub-domain (each on its own grid), and ii) an approximation ψ 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 ψ , the values of each trace of us on the boundary of each subdomain. We do it by solving an auxiliary problem 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.
The method of mothers for non-overlapping non-matching DDM
BREZZI, FRANCO;SANGALLI, GIANCARLO
2007-01-01
Abstract
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 −∆ u = g in Ω, our variables are i) the approximations of u in each sub-domain (each on its own grid), and ii) an approximation ψ 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 ψ , the values of each trace of us on the boundary of each subdomain. We do it by solving an auxiliary problem 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
