Summary
In this paper, we describe a way to compute accurate bounds on Jacobians 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.
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© 2011 Springer-Verlag Berlin Heidelberg
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Johnen, A., Remacle, JF., Geuzaine, C. (2011). Geometrical Validity of Curvilinear Finite Elements. 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_14
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DOI: https://doi.org/10.1007/978-3-642-24734-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24733-0
Online ISBN: 978-3-642-24734-7
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