A maximum principle for L 2-trace norms with an application to optimized schwarz methods

Abstract

Harmonic functions attain their pointwise maximum on the boundary of the domain. In this article, we analyze the relationship between various norms of nearly harmonic functions and we show that the trace norm is maximized on the boundary of the domain. One application is that the Optimized Schwarz Method with two subdomains converges for all Robin parameters α > 0. © 2009 Springer-Verlag Berlin Heidelberg.