Finite element method; high-order methods; mesh generation; Bézier functions; triangular elements
Abstract :
[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.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Johnen, Amaury ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Remacle, Jean-François; Université Catholique de Louvain - UCL > Institute of Mechanics, Materials and Civil Engineering (iMMC) > Applied mechanics and mathematics (MEMA)
Geuzaine, Christophe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Language :
English
Title :
Geometrical validity of high-order triangular finite elements
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