Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes |
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Authors: | Chen Shaochun; Shi Dongyang; Zhao Yongcheng |
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Institution: |
1 Department of Mathematics, Zhengzhou University, 450052, People's Republic of China
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Abstract: | In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition K/hK c0 > 0 is not satisfied, wherehK is the diameter of the element K and K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L2-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek. |
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Keywords: | anisotropic interpolation nonconforming finite element quasi-Wilson element |
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