  Anisotropic mesh quality measures and anisotropic mesh adaptation are studied
for polygonal meshes. Three sets of alignment and equidistribution measures are
developed, one based on least squares fitting, one based on generalized
barycentric mapping, and the other based on singular value decomposition of
edge matrices. Numerical tests show that all three sets of mesh quality
measures provide good measurements for the quality of polygonal meshes under
given metrics. Based on one of these sets of quality measures and using a
moving mesh partial differential equation, an anisotropic adaptive polygonal
mesh method is constructed for the numerical solution of second order elliptic
equations. Numerical examples are presented to demonstrate the effectiveness of
the method.
