How Good Is Sink Insertion?

Generating high quality meshes is one of the most important steps in many applications such as scientific computing. Sink insertion method is one of the mesh quality improvement methods that had been proposed recently. However, it is unknown whether this method is competitive to generate meshes with small number of elements. In this paper, we show that, given a two-dimensional polygonal domain with no small angles, the sink insertion method generates a well-shaped mesh with O(n) triangles, where n is the minimum number of triangles generated by any method with the same quality guarantee. We also show that the sink insertion method more likely can not guarantee the same result for a three-dimensional domain, while the other methods such as Delaunay refinement can achieve.