Preprint A668/2010
Technical Tools for Boundary Layers and Applications to Heterogeneous Coefficients
Marcus Sarkis | Dryja, Maksymilian
Keywords: discontinuous coefficients | FETI-DP algorithms | discrete harmonic extensions | boundary layer
We consider traces and discrete harmonic extensions on thin boundary layers. We introduce {\it sharp} estimates on how to control the $H^{1/2}-$ or $H^{1/2}_{00}-$ boundary norm of a finite element function by its energy in a thin layer and vice versa, how to control the energy of a discrete harmonic function in a layer by the $H^{1/2}$ or $H^{1/2}_{00}$ norm on the boundary. Such results play an important role in the analysis of domain decomposition methods in the presence of high-contrast media inclusions, small overlap and/or inexact solvers.