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Nonconforming rotated Q_1 element on non-tensor product anisotropic meshes
作者姓名:MAO Shipeng & SHI Zhongci Institute of Computational Mathematics  Academy of Mathematics and Systems Science  Chinese Academy of Sciences  PO Box  Beijing  China
作者单位:MAO Shipeng & SHI Zhongci Institute of Computational Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,PO Box 2719,Beijing 100080,China
基金项目:国家重点基础研究发展计划(973计划)
摘    要:In this paper, we consider the nonconforming rotated Q1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes, we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis.


Nonconforming rotated Q1 element on non-tensor product anisotropic meshes
MAO Shipeng & SHI Zhongci Institute of Computational Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,PO Box ,Beijing ,China.Nonconforming rotated Q_1 element on non-tensor product anisotropic meshes[J].Science in China(Mathematics),2006,49(10).
Authors:MAO Shipeng  SHI Zhongci
Abstract:In this paper, we consider the nonconforming rotated Q1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes, we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis.
Keywords:anisotropic  interpolation error  consistency error  nonconforming rotated Q1 element
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