Strong Regularity of a Family of Face-to-Face Partitions Generated by the Longest-Edge Bisection Algorithm

We examine the longest-edge bisection algorithm that chooses for bisection the longest edge in a given face-to-face simplicial partition of a bounded polytopic domain in R-d. Dividing this edge at its midpoint, we define a locally refined partition of all simplices that surround this edge. Repeating this process, we obtain a family F = {T-h}(h -> 0) of nested face-to-face partitions T-h. For d = 2, we prove that this family is strongly regular; i.e., there exists a constant C > 0 such that meas T >= Ch(2) for all triangles T is an element of T-h and all triangulations T-h is an element of F. In particular, the well-known minimum angle condition is valid.