Non-matching Grids and Lagrange Multipliers
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 −Δu = g in Ω, our variables are i) an approximation ψ h of u on the skeleton (the union of the interfaces of the sub-domains) on an independent grid (that could often be uniform), and ii) the approximations u h s of u in each subdomain Ω s (each on its own grid). The novelty is in the way to derive, from ψ h , the values of each trace of u h s on the boundary of each Ω s . We do it by solving an auxiliary problem on each ∂Ω s that resembles the mortar method but is more flexible. Optimal error estimates are proved under suitable assumptions.
KeywordsDomain Decomposition Domain Decomposition Method Piecewise Polynomial Accuracy Property Optimal Error Estimate
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