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Geometrical validity of curvilinear finite elements

Authors
Journal
Journal of Computational Physics
0021-9991
Publisher
Elsevier
Publication Date
Volume
233
Identifiers
DOI: 10.1016/j.jcp.2012.08.051
Keywords
  • Finite Element Method
  • High-Order Methods
  • Mesh Generation
  • Bézier Functions
Disciplines
  • Mathematics

Abstract

Abstract In this paper, we describe a way to compute accurate bounds on Jacobian determinants 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 Bézier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates.

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