  The properties and applications of superconvergence on size-guaranteed
Delaunay triangulation generated by bubble placement method (BPM), are studied
in this paper. First, we derive a mesh condition that the difference between
the actual side length and the desired length $h$ is as small as ${\cal
O}(h^{1+{\alpha}})$ $({\alpha}>0)$. Second, the superconvergence estimations
are analyzed on linear and quadratic finite element for elliptic boundary value
problem based on the above mesh condition. In particular, the mesh condition is
suitable for many known superconvergence estimations of different equations.
Numerical tests are provided to verify the theoretical findings and to exhibit
the superconvergence property on BPM-based grids.
