Numerical Estimates of Inequalities in H<sup>1/2</sup>

Ferdinand Kickinger, Sergei V. Nepomnyaschikh,
Ralf U. Pfau, and Joachim Schoberl

August 28, 1997

Abstract

The Sobolev norm H<sup>1/2</sup>(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 H<sup>1/2</sup>(Gamma)->H<sup>1</sup>(Omega) for the two
and three dimensional case, the discrete imbedding of H<sup>1/2</sup>(Gamma)
in L<sub>oo</sub>(Gamma) and of the norm estimates between
H<sup>1/2</sup>(Gamma) and H<sub>oo</sub><sup>1/2</sup>(Gamma).