Validity of Lagrange (Bézier) and rational Bézier quads of degree 2

Abstract : Finite elements of degree two or more are needed to solve various PDE problems. This paper discusses a method to validate such meshes for the case of quadrilateral elements of degree 2. The first section of this paper comes back to Bézier curve and Bézier quadrilateral patches of degree 2. The way in which a Bézier quad patch and a Q2 finite element quad are related is introduced. The two possible quads are discussed, the 9‐node (or complete) quad together with the 8‐node (or Serendipity) quad. A validity condition, the positivity of the Jacobian, is exhibited for these two elements. The discussion continues with a rational Bézier quad patch that can be used as a finite element. Extension to arbitrary degrees is given.
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Submitted on : Friday, September 13, 2019 - 3:07:44 PM
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Paul-Louis George, Houman Borouchaki. Validity of Lagrange (Bézier) and rational Bézier quads of degree 2. International Journal for Numerical Methods in Engineering, Wiley, 2014, 99 (8), pp.611-632. ⟨10.1002/nme.4696⟩. ⟨hal-02286200⟩

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