Quasi-optimal rates of convergence for the Generalized Finite Element Method in polygonal domains

Abstract

We consider a mixed-boundary-value/interface problem for the elliptic operator P = − ∑ ij ∂i(aij∂ju) = f on a polygonal domain Ω ⊂ R2 with straight sides. We endowed the boundary of Ω partially with Dirichlet boundary conditions u = 0 on ∂DΩ, and partially with Neumann boundary conditions ∑ ij νiaij∂ju = 0 on ∂NΩ. The coefficients aij are piecewise smooth… (More)
DOI: 10.1016/j.cam.2013.12.026

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