We present a new approach to quadrilateral mesh
refinement, which reduces the problem to its
structural core. The resulting problem formulation
belongs to a class of discrete problems, network
flow problems, which has been thoroughly
investigated and is well understood. The network-flow
model is flexible 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
refinement of mesh elements. We show that many
different variants of the general quadrilateral mesh
refinement problem are covered.
In particular, we present a novel strategy, which
provably finds a conformal refinement unless there
is none.
