| SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD |
| |
| 作者姓名： | 袁驷 和雪峰 |
| |
| 作者单位： | Department of Civil Engineering Tsinghua University，Beijing 100084，P. R. China，Department of Civil Engineering，Tsinghua University，Beijing 100084，P. R. China |
| |
| 摘 要： | Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
|
| 关 键 词： | 有限元法 自适应解 超收敛元能量投影 普通微分方程 ODE |
| 收稿时间： | 2005-10-09 |
| 修稿时间： | 2006-08-10 |
Self-adaptive strategy for one-dimensional finite element method based on element energy projection method |
| |
| Si Yuan Doctor,Xue-feng He.SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD[J].Applied Mathematics and Mechanics(English Edition),2006,27(11):1461-1474. |
| |
| Authors: | Si Yuan Doctor Xue-feng He |
| |
| Institution: | Department of Civil Engineering, Tsinghua University, Beijing 100084, P. R. China |
| |
| Abstract: | Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach. |
| |
| Keywords: | finite element method (FEM) self-adaptive solution super-convergence element energy projection ordinary differential equation (ODE) |
| 本文献已被 CNKI 维普 万方数据 SpringerLink 等数据库收录！ |
| 点击此处可从《应用数学和力学(英文版)》浏览原始摘要信息 |
| 点击此处可从《应用数学和力学(英文版)》下载免费的PDF全文 |
