Geometrical Validity of High-Order Triangular Finite Elements

in Engineering with Computers (2012)

This paper presents a method to compute accurate bounds on Jacobian determinants of high-order (curvilinear) triangular nite elements. This method can be used to guarantee that a curvilinear triangle is ... [more ▼]

This paper presents a method to compute accurate bounds on Jacobian determinants of high-order (curvilinear) triangular nite 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 e cient 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 B ezier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates. [less ▲]

Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011)

Book published by Université de Liège - Dépôt légal: D/2011/0480/31 (2011)

Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities

in International Journal for Numerical Methods in Engineering (2009), 79(11), 1309-1331