| 四维张量积二次矩形有限元最大模的超逼近 |
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| 引用本文： | 邓益军. 四维张量积二次矩形有限元最大模的超逼近[J]. 华东师范大学学报(自然科学版), 2011, 2011(4): 135-141. DOI: 10.3969/j.issn.1000-5641.2011.04.015 |
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| 作者姓名： | 邓益军 |
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| 作者单位： | 湖南涉外经济学院数学系,长沙,410205 |
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| 基金项目： | 湖南省高等学校科学研究一般项目 |
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| 摘 要： | 针对Poisson方程Dirichlet边值问题,首先建立了四维投影型插值算子,并应用它得到了正规剖分下四维张量积二次矩形有限元的弱估计.在此基础上,结合四维离散Green函数的估计,研究四维张量积二次矩形有限元解及梯度最大模的超逼近,获得了逐点意义下高精度的超收敛结果.
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| 关 键 词： | 椭圆边值问题 四维投影型插值算子 矩形有限元 弱估计 超逼近 |
| 收稿时间： | 2010-11-01 |
| 修稿时间： | 2011-02-01 |
Maximum-norm superapproximations for tensor-product quadraticrectangular finite elements in 4D |
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| DENG Yi-jun. Maximum-norm superapproximations for tensor-product quadraticrectangular finite elements in 4D[J]. Journal of East China Normal University(Natural Science), 2011, 2011(4): 135-141. DOI: 10.3969/j.issn.1000-5641.2011.04.015 |
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| Authors: | DENG Yi-jun |
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| Affiliation: | Department of Mathematics, Hunan International Economics University, Changsha 410205, China |
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| Abstract: | For Dirichlet boundary value problems of Poissonequations, an interpolation operator of projection type in 4D wasestablished. Then by using this operator, weak estimates fortensor-product quadratic rectangular finite elements over regularpartitions of a domain were obtained. Based on the obtained resultsand the estimates for the four-dimensional discrete Green'sfunction, some highly accuracy results of the maximum-normsuperapproximations of finite elements were derived. |
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| Keywords: | elliptic boundary value problem interpolation operator of projectiontype in 4D rectangular finite element weak estimate superapproximation |
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