Summary
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 high-order 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.
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Roca, X., Gargallo-Peiró, A., Sarrate, J. (2011). Defining Quality Measures for High-Order Planar Triangles and Curved Mesh Generation. In: Quadros, W.R. (eds) Proceedings of the 20th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24734-7_20
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DOI: https://doi.org/10.1007/978-3-642-24734-7_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24733-0
Online ISBN: 978-3-642-24734-7
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