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.