Algorithm of Super-Convergent in Two-Dimensional Finite Element of Lines Based on Improved Displacement Mode

TANG Yi-jun; LUO Jian-hui

doi:10.3879/j.issn.1000-0887.2013.08.005

Volume 34 Issue 8

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TANG Yi-jun, LUO Jian-hui. Algorithm of Super-Convergent in Two-Dimensional Finite Element of Lines Based on Improved Displacement Mode[J]. Applied Mathematics and Mechanics, 2013, 34(8): 815-823. doi: 10.3879/j.issn.1000-0887.2013.08.005

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Algorithm of Super-Convergent in Two-Dimensional Finite Element of Lines Based on Improved Displacement Mode

doi: 10.3879/j.issn.1000-0887.2013.08.005

Institute of Civil Engineering, Hunan University, Changsha 410082, P.R.China

Received Date: 2013-01-10
Rev Recd Date: 2013-06-25
Publish Date: 2013-08-15

Abstract

Abstract

Algorithm of super-convergent in two-dimensional finite element of lines (FEMOL) based on improved displacement mode is presented. An explicit analytical formula of super-convergent calculating was derived with the conditions of equilibrium equations stuictly met within the element, of which the displacement mode of high-order finite element of lines solution was expressed with that of a conventional finite element of lines solution. The new displacement mode was constructed with the sum of the displacement mode of conventional finite element of lines solution and that of high-order finite element of lines solution. Based on the linear shape function, the improved ordinary differential equations for FEMOL solution were derived in the rariation form. The super-convergent formula was used for this algorithm in both the pre-processing and post-processing to improve the accuracy of the solution and reduce the residual of balance equation, with the higher-order trial function added the original trial function. A calculation example is presented for Poisson’s equation of a two-dimensional problem, the convergence accuracy of the displacement and derivative at nodes and in elements is greatly improved.
- FEMOL,
- two-dimensional problem,
- pre-processing,
- displacement mode,
- Poisson’s equation,
- super-convergence

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References(12)

References

[1]	Zienkiewicz O C, Zhu J Z. The super-convergent patch recovery and a posteriori error estimates—partⅠ: the recovery technique[J].International Journal for Numerical Methods in Engineering,1992, 33(7):1331-1364.
[2]	陈传淼. 有限元超收敛构造理论[M]. 长沙: 湖南科学技术出版社, 2002.(CHEN Chuan-miao. Structure Theory of Super Convergence of Finite Elements [M]. Changsha: Hunan Science and Technology Press, 2002. (in Chinese))
[3]	袁驷. 从矩阵位移法看有限元应力精度的损失与恢复[J].力学与实践, 1998, 20(4):1-6.(YUAN Si. The loss and recovery of stress accuracy in FEM as seen from matrix displacement method[J].Mechanics and Practice,1998, 20(4): 1-6. (in Chinese))
[4]	袁驷, 王枚. 一维有限元后处理超收敛解答计算的EEP法[J].工程力学, 2004, 21(2):1-9.(YUAN Si, WANG Mei. An element-energy-projection method for post-computation of super-convergent solutions in one-dimensional FEM[J].Engineering Mechanics, 2004, 21(2): 1-9. (in Chinese))
[5]	袁驷, 王枚, 和雪峰. 一维C-1有限元超收敛解答计算的EEP法[J].工程力学, 2006 , 23(2):1-9.(YUAN Si, WANG Mei, HE Xue-feng. Computation of super-convergent solutions in one-dimensional C-1 FEM by EEP method[J].Engineering Mechanics,2006, 23(2):1-9. (in Chinese))
[6]	王玫, 袁驷. Timoshenko梁单元超收敛结点应力的EEP法计算[J]. 应用数学和力学, 2004 , 25(11):1124-1134.(WANG Mei, YUAN Si. Computation of super-convergent nodal sresses of Timoshenko beam elements by EEP method[J].Applied Mathematics and Mechanics,2004, 25(11):1124-1134.(in Chinese))
[7]	袁驷, 林永静. 二阶非自伴两点边值问题Galerkin有限元后处理超收敛解答计算的EEP法[J]. 计算力学学报, 2007, 24(2):142-147.(YUAN Si, LIN Yong-jing. An EEP method for post-computation of super-convergent solutions in one-dimensional Galerkin FEM for second order non-self-adjoint boundary value problem[J].Chinese Journal of Computational Mechanics,2007, 24(2): 142-147. (in Chinese))
[8]	袁驷, 王枚, 王旭. 二维有限元线法超收敛解答计算的EEP法[J]. 工程力学, 2007, 24(1): 1-10.（YUAN Si, WANG Mei, WANG Xu. An element-energy-projection method for super-convergence solutions in two-dimensional finite element method of lines[J].Engineering Mechanics,2007, 24(1): 1-10. (in Chinese)）
[9]	唐义军, 罗建辉.基于改进位移模式的一维C-1有限元超收敛算法[J].计算力学学报, 2012, 29(5):721-725.(TANG Yi-jun, LUO Jian-hui. Algorithm of super-convergent in one-dimensional C-1 FEM based on improved displacement mode[J].Chinese Journal of Computational Mechanics,2012, 29(5):721-725. (in Chinese)）
[10]	袁驷. 有限元线法[J]. 数值计算与计算机应用, 1992, 13(4): 252-260.（YUAN Si. The finite element method of lines[J].Journal on Numerical Methods and Computer Applications,1992, 13(4): 252-260. (in Chinese)）
[11]	唐义军, 罗建辉.基于改进位移模式的一维有限元超收敛算法[J].计算力学学报, 2012, 29(6):954-959.(TANG Yi-jun, LUO Jian-hui. Algorithm of super-convergent in one-dimensional FEM based on improved displacement mode[J].Chinese Journal of Computational Mechanics,2012, 29(6):954-959. (in Chinese))
[12]	LUO Jian-hui, LONG Yu-qiu, LIU Guang-dong. A new orthogonality relationship for orthotropic thin plate theory and its variational principle[J].Science in China Series G-Physics and Astronomy,2005, 38(3): 371-380.