A study of monitor functions for two-dimensional adaptive mesh generation

In this paper we study the problem of two-dimensional adaptive mesh generation using a variational approach and, specifically, the effect that the monitor function has on the resulting mesh behavior. The basic theoretical tools employed are Green's function for elliptic problems and the eigendecomposition of symmetric positive definite matrices. Based upon this study, a general strategy is suggested for how to choose the monitor function, and numerical results are presented for illustrative purposes. The three-dimensional case is also briefly discussed. It is noted that the strategy used here can be applied to other elliptic mesh generation techniques as well.