Engineering with Computers

, Volume 30, Issue 3, pp 375–382

Geometrical validity of high-order triangular finite elements

Original Article


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., its Jacobian determinant is strictly positive everywhere in its reference domain. It also provides an efficient way to measure the quality of 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.


Finite element method High-order methods Mesh generation Bézier functions 


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Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer Science, Montefiore Institute B28Université de LiègeLiègeBelgium
  2. 2.Institute of Mechanics, Materials and Civil EngineeringUniversité catholique de LouvainLouvain-la-NeuveBelgium

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