| 基于对偶混合变分原理的Signorini问题的数值模拟 |
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| 引用本文： | 王光辉,王烈衡.基于对偶混合变分原理的Signorini问题的数值模拟[J].计算物理,2002,19(2):149-154. |
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| 作者姓名： | 王光辉 王烈衡 |
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| 作者单位： | 1. 清华大学计算机科学与技术系, 北京 100084;2. 中科院计算数学与科学工程计算研究所, 科学与工程计算国家重点试验室, 北京 100080 |
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| 基金项目： | 国家自然科学基金(19672064)资助项目 |
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| 摘 要： | 基于Signorini问题的对偶混合变分形式,提出了一种非协调有限元逼近格式,证明了离散的B-B条件,获得了Raviart-Thomas(k=0)有限元逼近的误差界O(h3/4),并且Uzawa型算法对协调与非协调有限元逼近格式进行了数值求解.根据数值结果的分析和比较,表明应用非协调有限元逼近格式求解更有效.
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| 关 键 词： | Signorini问题 对偶混合变分形式 Raviart-Thomas元 非协调有限元 Uzawa算法 |
| 文章编号： | 1001-246X(2002)02-0149-06 |
| 收稿时间： | 2000-07-24 |
| 修稿时间： | 2000年7月24日 |
NUMERICAL MODELING OF SIGNORINI PROBLEM BASED ON DUAL MIXED VARIATIONAL PRINCIPLE |
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| WANG Guang-hui,WANG Lie-heng.NUMERICAL MODELING OF SIGNORINI PROBLEM BASED ON DUAL MIXED VARIATIONAL PRINCIPLE[J].Chinese Journal of Computational Physics,2002,19(2):149-154. |
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| Authors: | WANG Guang-hui WANG Lie-heng |
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| Institution: | 1. Department of Computer Science and Technology, Tsinghua University, Beijing 100084, P R China;2. Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, State Key Labora |
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| Abstract: | Based on the dual mixed variational formulation for the Signorini problem,a nonconforming finite element method is proposed.The discrete B-B condition is confirmed and the error estimation O(h3/4)for Raviart-Thomas(k=0)finite element is achieved.A Uzawa type algorithm is used for solving the Signorini problem which is discretized by conforming finite element method as well as nonconforming finite element method.The accuracy and efficiency of both are demonstrated by numerical results.By contrast to the conforming one,nonconforming method is more cost-effective. |
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| Keywords: | Signorini problem dual mixed variational formulation Raviart-Thomas element nonconforming finite element Uzawa algorithm |
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