Some remarks on the constant in the strengthened CBS inequality: Estimate for hierarchical finite element discretizations of elasticity problems
✍ Scribed by Michael Jung; Jean-François Maitre
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 253 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0749-159X
No coin nor oath required. For personal study only.
✦ Synopsis
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 (CBS) inequality in the cases of two-level hierarchical piecewise-linear/piecewise-linear and piecewise-linear/piecewisequadratic 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 CBS inequality on the Poisson's ratio. Furthermore, numerically determined bounds of the constant in the CBS inequality are given for plane linear elasticity problems discretized by means of arbitrary triangles and for three-dimensional elasticity problems discretized by means of tetrahedral elements. Finally, the robustness of iterative solvers for elasticity problems is discussed briefly.