| 一维Ritz有限元超收敛计算的EEP法简约格式的误差估计 |
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| 引用本文： | 袁驷,邢沁妍.一维Ritz有限元超收敛计算的EEP法简约格式的误差估计[J].工程力学,2014,31(12):1. |
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| 作者姓名： | 袁驷 邢沁妍 |
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| 作者单位： | 清华大学土木工程系,土木工程安全与耐久教育部重点实验室,北京 100084 |
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| 基金项目： | 国家自然科学基金项目(51378293,51078199,50678093,50278046) |
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| 摘 要： | 该文对一维问题Ritz有限元后处理超收敛计算的EEP(单元能量投影)法简约格式给出误差估计的数学证明,即对足够光滑问题的(>1)次单元的有限元解答,采用EEP法简约格式计算得到的单元内任一点位移和应力(导数)超收敛解均可以达到的收敛阶,即位移比常规有限元解的收敛阶至少高一阶,而应力则至少高二阶。
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| 关 键 词： | 有限元 一维问题 超收敛 收敛阶 单元能量投影 |
| 收稿时间： | 2014-09-20 |
AN ERROR ESTIMATE OF EEP SUPER-CONVERGENT SOLUTIONS OF SIMPLIFIED FORM IN ONE-DIMENSIONAL RITZ FEM |
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| Affiliation: | Department of Civil Engineering, Tsinghua University, Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Beijing 100084, China |
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| Abstract: | For one-dimensional problems of Ritz Finite Element Method (FEM), an error estimate is presented for the simplified form of the Element Energy Projection (EEP) method used for super-convergence computation in post-processing stage of FEM. The mathematical analysis proves that for elements of degree (>1) with sufficiently smooth solutions, EEP solutions of the simplified form are capable of producing super-convergent solutions with convergence order of for both displacements and stresses at any point on an element, i.e. EEP simplified form obtains at least one order higher displacements and at least two order higher stresses than conventional FEM solutions. |
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