On the discrete core of quadrilateral mesh refinement

We present a new approach to quadrilateral mesh refinement, which reduces t he problem to its structural core. The resulting problem formulation belong s to a class of discrete problems, network-flow problems, which has been th oroughly investigated and is well understood. The network-flow model is fle xible enough to allow the simultaneous incorporation of various aspects suc h as the control of angles and aspect ratios, local density control, and te mplates (meshing primitives) for the internal refinement of mesh elements. We show that many different variants of the general quadrilateral mesh-refi nement problem are covered. In particular, we present a novel strategy, whi ch provably finds a conformal refinement unless there is none. Copyright (C ) 1999 John Wiley & Sons, Ltd.