Reference : Geometrical Validity of High-Order Triangular Finite Elements
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
http://hdl.handle.net/2268/129806
Geometrical Validity of High-Order Triangular Finite Elements
English
Johnen, Amaury mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE) >]
Remacle, Jean-François mailto [Université Catholique de Louvain - UCL > Institute of Mechanics, Materials and Civil Engineering (iMMC) > Applied mechanics and mathematics (MEMA) > >]
Geuzaine, Christophe mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE) >]
7-Dec-2012
Engineering with Computers
Yes (verified by ORBi)
International
0177-0667
1435-5663
[en] Finite element method ; high-order methods ; mesh generation ; Bézier functions ; triangular elements
[en] This paper presents a method to compute accurate bounds on Jacobian
determinants of high-order (curvilinear) triangular nite elements. This method can
be used to guarantee that a curvilinear triangle is geometrically valid, i.e., that its
Jacobian determinant is strictly positive everywhere in its reference domain. It also
provides an e cient way to measure the quality the triangles. The key feature of the
method is to expand the Jacobian determinant using a polynomial basis, built using
B ezier functions, that has both properties of boundedness and positivity. Numerical
results show the sharpness of our estimates.
http://hdl.handle.net/2268/129806

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