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二维粘弹性问题的广义差分法及其数值模拟

李焕荣,罗振东,李潜,   

  1. 重庆工商大学理学院,北京交通大学理学院,山东师范大学数学科学学院 重庆400067,北京100044,济南250014
  • 出版日期:2007-03-14 发布日期:2007-03-14

李焕荣,罗振东,李潜,. 二维粘弹性问题的广义差分法及其数值模拟[J]. 计算数学, 2007, 29(3): 251-262.

GENERALIZED DIFFERENCE METHODS AND NUMERICAL SIMULATION FOR TWO-DIMENSIONAL VISCOELASTIC PROBLEMS

  1. Li Huanrong (School of Sciences,Chongqing Technology and Business University,Chongqing 400067,China) Luo Zhendong (School of Sciences,Beijing Jiaotong University,Beijing 100044,China) Li Qian (School of Mathematics,Shandong Teacher's University,Jinan 250014,China)
  • Online:2007-03-14 Published:2007-03-14
本文利用广义差分法讨论了二维粘弹性问题.建立了二维粘弹性问题的广义差分格式,给出了一种新的初始值近似,证明了广义差分解的最优L~p估计和W~1,p(2≤p≤∞)模估计,同时得到了广义的Ritz—Volterra投影和广义差分解之间的超收敛的W~1,p(2≤p≤∞)模的误差估计.最后给出了一个数值算例以验证该方法的可行性.
In this paper,generalized difference methods(GDM)for two-dimensional viscoelastic problems are proposed and analyzed.The special initial values are given in the generalized difference scheme,so we obtain optimal error estimates in L~p and W~1,P(2≤p≤∞)as well as some superconvergence estimates in W~1,P(2≤p≤∞)between the GDM solution and the generalized Ritz-Volterra projection of the exact solution.And finally,a numerical example is given.
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