On the radius Edge Condition in the Control Volume Method

Gary L. Miller, Dafna Talmor, Shang-Hua Teng and Noel Walkington
Carnegie-Mellon technical report, math department.

92k compressed postscript

Abstract: In this paper we show that the control volume algorithm for the solution of Poisson's equation in three dimensions will converge when the mesh contains very flat tetrahedra(slivers). These tetrahedra are characterized by the fact that they have modest ratios of diameter to shortest edge, but large circum to inscribed sphere radius ratios, so may have poor interpolation properties. Elimination of slivers is a notoriously difficult problem for automatic mesh generation algorithms. We also show that a discrete Poincare inequality will continue to hold in the presence of slivers.