Reference : Geometrical Validity of Curvilinear Finite Elements
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Engineering, computing & technology : Computer science
http://hdl.handle.net/2268/128340
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, J.-F. []
Geuzaine, Christophe mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE) >]
15-Jan-2013
Journal of Computational Physics
Academic Press
233
359-372
Yes (verified by ORBi)
International
0021-9991
1090-2716
[en] Finite element method ; high-order methods ; mesh generation ; Bézier functions
[en] In this paper, we describe a way to compute accurate bounds on Jacobian de- terminants of curvilinear polynomial finite elements. Our condition enables to guarantee that an element 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 distortion of curvilinear elements. 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/2268/128340

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