Inclusion method of optimal constant with quadratic convergence for $H_0^1$-projection error estimates and its applications
Inclusion method of optimal constant with quadratic convergence for $H_0^1$-projection error estimates and its applications
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$H_0^1$-投影误差估计的二次收敛最优常数包含方法及其应用
DOI：
10.1016/j.cam.2022.114521
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发表时间：
2023
影响因子：
2.4
通讯作者：
Takehiko Kinoshita and Yoshitaka Watanabe and Nobito Yamamoto and Mitsuhiro T. Nakao
中科院分区：
文献类型：
--
作者：
Yuki Nishida;Sennosuke Watanabe;Akiko Fukuda and Yoshihide Watanabe;宮島信也;H. Sano;宮島信也;Takehiko Kinoshita and Yoshitaka Watanabe and Nobito Yamamoto and Mitsuhiro T. Nakao
给出了有限次多项式空间H01-投影的二阶误差估计的最优常数的区间包含方法。这些常数可用于拉格朗日型有限元方法的误差估计。此外，所提出的先验误差估计也适用于验证非线性椭圆型方程解的残差迭代技术。文中给出了一些有限元数值算例，并与其他方法进行了比较，证实了本文结果对偏微分方程组数值验证方法的实际有效性。
We present an interval inclusion method for optimal constants of second-order error estimates of H 0 1-projections to finite-degree polynomial spaces. These constants can be applied to error estimates of the Lagrange-type finite element method. Moreover, the proposed a priori error estimates are applicable to residual iteration techniques for the verification of solutions to nonlinear elliptic equations. Some numerical examples by the finite element method will be shown for comparison with other approaches, which confirm us the actual usefulness of the results in this paper for the numerical verification method for PDEs.