In this paper, we describe a way to compute accurate bounds on Jaco-bians of curvilinear finite elements of all kinds. Our condition enables to guarantee that an element is geometrically valid, i.e., that its Jacobian is strictly positive everywhere in its reference domain. It also provides an efficient way to measure the distortion of curvilinear elements. The key feature of the method is to expand the Jacobian using a polynomial basis, built using Bézier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates.
CITATION STYLE
Johnen, A., Remacle, J. F., & Geuzaine, C. (2011). Geometrical validity of curvilinear finite elements. In Proceedings of the 20th International Meshing Roundtable, IMR 2011 (pp. 255–271). Kluwer Academic Publishers. https://doi.org/10.1007/978-3-642-24734-7_14
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