* M. Jung and J. F. Maitre*

** Some Remarks on the Constant in the Strengthened C.B.S. Inequality:
Application to h- and p-Hierarchical
Finite Element Discretizations of Elasticity Problems
**

Preprint SFB393/97-15, Sonderforschungsbereich 393, TU Chemnitz-Zwickau

For a class of two-dimensional boundary value problems including diffusion
and elasticity problems it is proved that the constants in the corresponding
strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality in the cases of
*h*-hierarchical and *p*-hierarchical finite element
discretizations
with triangular meshes differ by the factor 0.75.
For plane linear elasticity problems and triangulations with right isosceles
triangles formulas are presented that show the dependence of the constant in
the C.B.S. inequality on the Poisson's ratio. Furthermore, numerically determined
bounds of the constant in the C.B.S.~inequality are given for
three-dimensional elasticity problems discretized by means of tetrahedral
elements.
Finally, the robustness of iterative solvers for elasticity
problems is discussed briefly.