Localization of trace norms in two and three dimensions

Abstract

We extend a localization result for the $H^{1/2}$ norm by B. Faermann to a wider class of subspaces of $H^{1/2}(\Gamma )$, and we prove an analogous result for the $H^{-1/2}(\Gamma )$ norm, $\Gamma$ being the boundary of a bounded polytopal domain $\Omega$ in ${\mathbb{R}}^n$, $n=2,3$. As a corollary, we obtain equivalent, better localized, norms for both $H^{1/2}(\Gamma )$ and $H^{-1/2}(\Gamma )$, which can be exploited, for instance, in the design of preconditioners or of stabilized methods.

arXiv comment8 pages, no figures