The method of mothers for non-overlapping non-matching DDM
نویسندگان
چکیده
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 uh of u in each sub-domain Ωs (each on its own grid), and ii) an approximation ψh 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 ψh, the values of each trace of uh on the boundary of each Ω s. We do it by solving an auxiliary problem on each ∂Ωs 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 [7].
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عنوان ژورنال:
- Numerische Mathematik
دوره 107 شماره
صفحات -
تاریخ انتشار 2007