Robust distortion metric for quadratic triangular 2D finite elements

Finite element mesh quality can greatly affect finite element analysis. Generally, it has been accepted that element size and shape influence the quality and computational efficiency of a finite element solution. Measures of linear element shape such as aspect ratio, angles, and others (Babuska and Aziz, 1979, and Barlow, 1978) have been developed and tested for many years. The main function of these distortion metrics is to detect poorly shaped elements that may either slow down the convergence rate of the analysis or even cause it to diverge or give incorrect answers. While much work has been done in defining element distortion for linear elements, very little work has gone into similar work for quadratic elements. This paper introduces a robust element quality metric, based on the new concept of mid-node admissible spaces for 2D quadratic triangular finite elements. The metric is based on the Jacobian determinant over the entire element, without requiring that it actually be computed everywhere on the element. In terms of CPU time, it is relatively inexpensive - especially for mildly distorted elements. It may also be noted that these computations are generally only needed near the boundary of the mesh, where curved elements are used to better approximate the geometry. Linear measures can be used throughout the interior of the mesh, where the sides are straight. This metric is shown to be able to detect elements of poor quality that other distortion metrics do not detect. It can also approve elements of good quality regardless of how distorted they may appear.