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) >]
2014
Engineering with Computers
30
3
375-382
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 finite 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 efficient 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 Bézier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates.
http://hdl.handle.net/2268/129806
10.1007/s00366-012-0305-7

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