Summary
We consider traces and discrete harmonic extensions on thin boundary layers. We introduce 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.
* This work was supported in part by the Polish Sciences Foundation under grant NN201006933.
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Dryja*, M., Sarkis, M. (2011). Technical Tools for Boundary Layers and Applications to Heterogeneous Coefficients. In: Huang, Y., Kornhuber, R., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11304-8_22
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DOI: https://doi.org/10.1007/978-3-642-11304-8_22
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