Superconvergence of Solution Derivatives for the Shortley–Weller Difference Approximation of Poisson's Equation. II. Singularity Problems
Superconvergence of Solution Derivatives for the Shortley–Weller Difference Approximation of Poisson's Equation. II. Singularity Problems
复制标题
泊松方程的 Shortley–Weller 差分逼近解导数的超收敛 II。
DOI：
10.1081/nfa-120022918
复制
发表时间：
2003
影响因子：
1.2
通讯作者：
Tetsuro Yamamoto
中科院分区：
文献类型：
--
作者：
Zi;Hsin‐Yun Hu;Qing Fang;Tetsuro Yamamoto
Li， Z. C., Yamamoto， T., Fang， Q. ([2003]): Poisson方程的Shortley-Weller差分逼近的解导数的超收敛性，第1部分：光滑性问题。J. Comp. and apple。数学。152(2):307-333)，这是探索边界附近无界导数的超收敛性。通过使用Yamamoto (Yamamoto， T.（[2002]）中提出的拉伸函数：一致和不一致有限差分格式的收敛性和加速技术。J. Comp.苹果。数学。140:849-866)，二阶超收敛的解导数可以建立。并通过数值实验对误差分析进行了验证。本文的分析方法不同于Li， Z. C., Yamamoto， T., Fang， Q.（[2003]）。本文还给出了双线性有限元法和九节点有限差分法的超收敛性分析。
Abstract This is a continued analysis on superconvergence of solution derivatives for the Shortley–Weller approximation in Li (Li, Z. C., Yamamoto, T., Fang, Q. ([2003]): Superconvergence of solution derivatives for the Shortley–Weller difference approximation of Poisson's equation, Part I. Smoothness problems. J. Comp. and Appl. Math. 152(2):307–333), which is to explore superconvergence for unbounded derivatives near the boundary. By using the stretching function proposed in Yamamoto (Yamamoto, T. ([2002]): Convergence of consistant and inconsistent finite difference schemes and an acceleration technique. J. Comp. Appl. Math. 140:849–866), the second order superconvergence for the solution derivatives can be established. Moreover, numerical experiments are provided to support the error analysis made. The analytical approaches in this article are non-trivial, intriguing, and different from Li, Z. C., Yamamoto, T., Fang, Q. ([2003]). This article also provides the superconvergence analysis for the bilinear finite element method and the finite difference method with nine nodes.