Geometrical validity of curvilinear finite elements

JOURNAL OF COMPUTATIONAL PHYSICS

卷:233

Article

Johnen, A.¹  Remacle, J. -F.²  Geuzaine, C.¹ 

[1] Univ Liege, Dept Elect Engn & Comp Sci, Montefiore Inst B28, B-4000 Liege, Belgium

[2] Catholic Univ Louvain, Inst Mech Mat & Civil Engn iMMC, B-1348 Louvain, Belgium

关键词: Finite element method;    High-order methods;    Mesh generation;    Bezier functions;   

DOI  :  10.1016/j.jcp.2012.08.051

来源: Elsevier

【 摘 要 】

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 Bezier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free