Defining Quality Measures for High-Order Planar Triangles and Curved Mesh Generation

We present a technique to extend any Jacobian based quality measure for linear elements to high-order isoparametric planar triangles of any interpolation degree. The extended quality measure is obtained as the inverse of the distortion of the high-order element with respect to an ideal element. To measure the highorder distortion, we integrate on the curved element the inverse of the Jacobian based quality measure. Thus, we can proof that if the Jacobian based quality is invariant under a particular affine mapping, then the resulting quality measure is also invariant under that mapping. In addition, we check that the quality measure detects non-valid and low-quality high-order elements. Finally, we present and test an approach to generate curved meshes by minimizing the high-order distortion measure of the elements.