Algebraic mesh quality metrics for unstructured initial meshes

Explicit formulas for size, shape, skew, and combined mesh quality metrics are given for triangular, tetrahedral, quadrilateral, and hexahedral finite elements. The formulas are examples of abstractly defined metrics whose essential properties serve to guide the formulation of effective metrics. Effectiveness is demonstrated via comparisons with other metrics, contour plots, and analysis of particular meshes. (C) 2002 Elsevier Science B.V. All rights reserved.