| NODAL O（h^4）-SUPERCONVERGENCE IN 3D BY AVERAGING PIECEWISE LINEAR,BILINEAR, AND TRILINEAR FE APPROXIMATIONS |
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| 作者姓名： | Antti Hannukainen Sergey Korotov Michal Krizek |
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| 作者单位： | [1]Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 Espoo, Finland [2]Department of Mathematics, Tampere University of Technology, P.O. Box 553, FI 33101 Tampere, Finland [3]Institute of Mathematics, Academy of Sciences, Zitna 25, CZ 115 67 Prague 1, Czech Republic |
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| 基金项目： | Acknowledgements. The authors are thankful to Jan Brandts from the University of Amsterdam for many useful comments on the paper. The first author was supported by Project no. 211512 from the Academy of Finland. The second author was supported by Academy Research Fellowship no. 208628 and Project no. 124619 from the Academy of Finland. The third author was supported by Grant IAA 100190803 of the Academy of Sciences of the Czech Republic and Institutional Research Plan AVOZ 10190503. |
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| 摘 要： | We construct and analyse a nodal O（h^4）-superconvergent FE scheme for approximating the Poisson equation with homogeneous boundary conditions in three-dimensional domains by means of piecewise trilinear functions. The scheme is based on averaging the equations that arise from FE approximations on uniform cubic, tetrahedral, and prismatic partitions. This approach presents a three-dimensional generalization of a two-dimensional averaging of linear and bilinear elements which also exhibits nodal O（h^4）-superconvergence （ultracon- vergence）. The obtained superconvergence result is illustrated by two numerical examples.
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| 关 键 词： | 有限元逼近 分段线性 超收敛 双线性 平均 三维 节块 泊松方程 |
NODAL O（h^4）-SUPERCONVERGENCE IN 3D BY AVERAGING PIECEWISE LINEAR,BILINEAR, AND TRILINEAR FE APPROXIMATIONS |
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| Antti Hannukainen,Sergey Korotov,Michal Krizek.NODAL O（h^4）-SUPERCONVERGENCE IN 3D BY AVERAGING PIECEWISE LINEAR,BILINEAR, AND TRILINEAR FE APPROXIMATIONS[J].Journal of Computational Mathematics,2010(1):1-10. |
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| Abstract: | Higher order error estimates, Tetrahedral and prismatic elements, Supercon-vergence, Averaging operators. |
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| Keywords: | Higher order error estimates Tetrahedral and prismatic elements Supercon-vergence Averaging operators |
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