Maximum-norm superapproximations for tensor-product quadratic rectangular finite elements in 4D
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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.Abstract: For Dirichlet boundary value problems of Poisson equations, an interpolation operator of projection type in 4D was established. Then by using this operator, weak estimates for tensor-product quadratic rectangular finite elements over regular partitions of a domain were obtained. Based on the obtained results and the estimates for the four-dimensional discrete Green's function, some highly accuracy results of the maximum-norm superapproximations of finite elements were derived.
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