Anisotropic mesh quality measures and adaptation for polygonal meshes

Abstract

Anisotropic mesh quality measures and adaptation are studied for convex polygonal meshes. Three sets of alignment and equidistribution measures are developed, based on least squares fitting, generalized barycentric mappings, and the singular value decomposition, respectively. Numerical tests show that all three sets of mesh quality measures provide good measurements for the quality of polygonal meshes under given anisotropic metrics. Based on the second set 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.