On the discrete core of quadrilateral mesh refinement

We present a new approach to quadrilateral mesh re nement, which reduces the problem to its structural core. The resulting problem formulation belongs to a class of discrete problems, network- ow problems, which has been thoroughly investigated and is well understood. The network- ow model is exible enough to allow the simultaneous incorporation of various aspects such as the control of angles and aspect ratios, local density control, and templates (meshing primitives) for the internal re nement of mesh elements. We show that many di erent variants of the general quadrilateral mesh-re nement problem are covered. In particular, we present a novel strategy, which provably nds a conformal re nement unless there is none