| 一类双曲型积分微分问题有限元逼近的超收敛估计 |
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| 引用本文： | 公敬,杨晓忠,李潜. 一类双曲型积分微分问题有限元逼近的超收敛估计[J]. 工程数学学报, 2005, 22(3): 413-419 |
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| 作者姓名： | 公敬 杨晓忠 李潜 |
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| 作者单位： | 华北电力大学(北京)科学与工程计算研究所,北京,102206;山东师范大学数学系,济南,250014 |
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| 基金项目： | Foundations for University Key Teacher by the Ministry of Educationthe Science Foundations for Young Teachers of North China Electric Power University． |
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| 摘 要： | 本文研究双曲型积分微分方程的半离散有限元逼近格式的超收敛估计.基于一种新的初值近似,得到了有限元解与精确解的Ritz-Volterra投影的Ws,p(Ω)模的如下超收敛估计k＞1,s=0,2≤p≤∞时,超收敛1阶;k＞1,s=1,2≤p＜∞时,超收敛2阶;k＞1,s=1,p=∞时,几乎超收敛2阶;k=1,s=1,2≤p≤∞时,超收敛1阶.
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| 关 键 词： | 超收敛 双曲型积分微分方程 有限元 |
Superconvergence of a Finite Element Method for a Kind of Hyperbolic Integro-differential Problems |
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| GONG Jing,YANG Xiao-zhong,LI Qian. Superconvergence of a Finite Element Method for a Kind of Hyperbolic Integro-differential Problems[J]. Chinese Journal of Engineering Mathematics, 2005, 22(3): 413-419 |
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| Authors: | GONG Jing YANG Xiao-zhong LI Qian |
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| Abstract: | In this paper, we study the superconvergence of a semi-discrete finite element scheme for hyperbolic integro-differential problems using any degree of elements. The scheme is based on introducing a new way of approximating initial conditions. We obtain several superconvergence results for the error between the approximate solution and the RitzVolterra projection of the exact solution. For k＞1, we obtain first order gain in Lp (2≤p≤∞) norm, second order in W1,p (2≤p＜∞) norm and almost second order in W1,∞ norm. For k = 1, we obtain first order gain in W1,p (2≤p≤∞) norm. |
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| Keywords: | superconvergence hyperbolic integro-differential equation finite element scheme |
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