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Geometrical Validity of Curvilinear Finite Elements

Johnen, A., J.-F. Remacle and C. Geuzaine

20th International Meshing Roundtable, Springer-Verlag, pp.255-270, October 23-26 2011


20th International Meshing Roundtable
Paris, France
October 23-26, 2011

Universite de Liege, Department of Electrical Engineering and Computer Science, Montefiore Institute B28, Grande Traverse 10, 4000 Liege, Belgium, Institute of Mechanics, Materials and Civil Engineering, Universit catholique de Louvain, Avenue Georges-Lematre 4, 1348 Louvain-la-Neuve, Belgium
Email: {ajohnen, cgeuzaine},

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 Bezier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates.

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