DOI link for Sliver exudation
Sliver exudation book
The quality measure naturally optimized by Delaunay refinement algorithms is the radiusedge ratio. Although it identifies all skinny triangles, the radius-edge ratio fails to screen out some sliver tetrahedra, so standard Delaunay refinement methods guarantee that they can remove most kinds of bad tetrahedra, but not all. Slivers have dihedral angles arbitrarily close to both 180◦ and 0◦, and thereby poison both the discretization error and the conditioning of the stiﬀness matrix in the finite element method. Some of the quality measures we describe in Section 1.7-namely, the aspect ratio and the volume-length measure-give poor scores to all skinny tetrahedra. Unfortunately, these measures are not easy to optimize. It is notoriously diﬃcult to devise algorithms that oﬀer a mathematical guarantee that slivers will not survive.