Numerical Estimates of Inequalities in H1/2

Ferdinand Kickinger
Johannes Kepler University
Institut für Mathematik
A-4040 Linz, Altenbergerstrasse 69, Austria

Sergej V. Nepomnyaschikh
Computing Center
Siberian Branch of Russian Academy of Sciences
Novosibirsk, 630090, Russia

Ralf U. Pfau
Johannes Kepler University
Institut für Mathematik
A-4040 Linz, Altenbergerstrasse 69, Austria

Joachim Schoberl
Johannes Kepler University
Institut für Mathematik
A-4040 Linz, Altenbergerstrasse 69, Austria

Abstract

The Sobolev norm H1/2(Gamma) plays a key role in domain decomposition (DD) techniques. For the efficiency of DD-preconditioners the quantitative values of several constants is important.

The goal of this paper is the numerical investigation of the constants in explicit extensions H1/2(Gamma)->H1(Omega) for the two and three dimensional case, the discrete imbedding of H1/2(Gamma) in Loo(Gamma) and of the norm estimates between H1/2(Gamma) and Hoo1/2(Gamma).


Contributed November 27, 1997.