| 矩形有限元分析 |
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| 引用本文： | 陈宏森. 矩形有限元分析[J]. 湘潭大学自然科学学报, 1989, 11(4): 1-11 |
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| 作者姓名： | 陈宏森 |
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| 作者单位： | 湘潭大学数学系 |
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| 摘 要： | 本文讨论Poisson方程Dirichlet边值问题并证明了在拟一致矩形剖分下双线性有限元解的超收敛性质与外推估计,井由此得出非协调的Wilson有限元的相应性质。接着本文还证明了双二次有限元在拟一致剖分下超收敛性及高阶误差渐近展开。本文的结果包含了文[5]的结论,同时推广了[1]、[6]的结果。
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| 关 键 词： | 双线性元 超收敛 矩形剖分 有限元 |
ANALYSIS OF RECTENGULAR FINITE ELEMENT |
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| Cheng Hongsen. ANALYSIS OF RECTENGULAR FINITE ELEMENT[J]. Natural Science Journal of Xiangtan University, 1989, 11(4): 1-11 |
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| Authors: | Cheng Hongsen |
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| Affiliation: | Department of Mathematics |
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| Abstract: | In this paper, the extrapolation estimats of bilinear finite element and wilson's nonconforminf finite element approximations are shown forDirichlet problems of possion equation under quasi-uniforming rectangularmeshes. A superconvergence estimate of biquadratic finite element solutionare also proved under same meshes. Furthermore, for uniforming meshesthe approximation error of biquatratic element can be expanded in theform u(z) - u_2~h(z)=w(z)h~4 O(h~e|Lnh|)at the vertices of all elements of the meshes. |
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| Keywords: | quas-uniforming rectangular meshes bilinear finite element wilson element biquadratic element superconvergence extrapo-lation |
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