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

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