Mid-node admissible spaces for quadratic triangular 2D finite elements with one edge curved

A robust element distortion metric, based on the new concept of mid-node admissible spaces, for two-dimensional quadratic triangular finite elements is developed. The metric is based on the Jacobian determinant over the entire element, without requiring that it actually be computed everywhere on the element. The metric is relatively inexpensive to compute, especially for mildly distorted elements. The metric is able to detect elements of poor quality that other distortion metrics fail to detect. It also has the ability to approve elements of good quality regardless of the extent to which they may appear geometrically distorted.