Mathematical Analysis for Quadrilateral Rotated $Q_1$ Element II: Poincarè Inequality and Trace Inequality

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Abstract

This is the second part of the paper for the mathematical study of nonconforming rotated $Q_1$ element (NR$Q_1$ hereafter) on arbitrary quadrilateral meshes. Some Poincarè Inequalities are proved without assuming the quasi-uniformity of the mesh subdivision. A discrete trace inequality is also proved.

Keywords:

Quadrilateral rotated $Q_1$ element Poincarè inequality Trace inequality.
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Mathematical Analysis for Quadrilateral Rotated $Q_1$ Element II: Poincarè Inequality and Trace Inequality. (2003). Journal of Computational Mathematics, 21(3), 277-286. https://global-sci.com/index.php/JCM/article/view/11553