Reference : Geometrical validity of curvilinear finite elements
Scientific congresses and symposiums : Paper published in a book
Engineering, computing & technology : Multidisciplinary, general & others
http://hdl.handle.net/2268/113717
Geometrical validity of curvilinear 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) >]
25-Oct-2011
Proceedings of the 20th International Meshing Roundtable
William Roshan, Quadros
Springer
Yes
No
International
978-3-642-24733-0
20th International Meshing Roundtable
du 23 octobre au 26 octobre 2011
Paris
France
[en] finite element method ; high-order methods ; mesh generation ; Bézier functions
[en] 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.
http://hdl.handle.net/2268/113717
10.1007/978-3-642-24734-7_14

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