A p-type superconvergent recovery method for FE analysis on boundary value problems of second-order nonlinear ordinary differential equations

被引：0
|
作者：
Ye K.-S. [1 ]
Qiu T.-Z. [1 ]
机构：
[1] Department of Civil Engineering, Tsinghua University, Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Beijing
来源：
Gongcheng Lixue/Engineering Mechanics | 2019年 / 36卷 / 12期
关键词：
Boundary value problem; Finite element method; Nonlinearity; Ordinary differential equation; P-type superconvergent recovery;
D O I：
10.6052/j.issn.1000-4750.2019.01.0005
中图分类号：
学科分类号：
摘要：
It presents a p-type superconvergent recovery method for the finite element analysis on two-point boundary value problems (BVPs) of second-order nonlinear ordinary differential equations. Based on the superconvergence property of nodal values, a linear two-point BVP which approximately governs the solutions on each element is set up by setting the elements' end values in FE solutions as boundary conditions and linearizing the governing differential equations via Taylor expansion technique. This local linear BVP is solved by using a higher order element from which the solution on each element is recovered. This method is a post-processing approach and the recovery computation is carried out on each element separately. It can improve the accuracy and convergence rate of the solutions significantly with a small computation. Numerical examples demonstrate that this method is efficient, reliable and potential. © 2019, Engineering Mechanics Press. All right reserved.
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页码：7 / 14
页数：7
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  • [1] Zienkiewicz O.C., Zhu J.Z., The superconvergent patch recovery and a posteriori error estimates. Part 1: The Recovery technique, International Journal for Numerical Methods in Engineering, 33, 7, pp. 1331-1364, (1992)
  • [2] Zienkiewicz O.C., Zhu J.Z., The superconvergent patch recovery and a posteriori error estimate. Part 2: Error Estimates and adaptivity, International Journal for Numerical Methods in Engineering, 33, 7, pp. 1365-1382, (1992)
  • [3] Boroomand B., Zienkiewicz O.C., Recovery by equilibrium in patches (REP), International Journal for Numerical Methods in Engineering, 40, 1, pp. 137-164, (1997)
  • [4] Stein E., Ohnimus S., Equilibrium method for postprocessing and error estimation in the finite element method, Computer Assisted Mechanics and Engineering Sciences, 4, 3-4, pp. 645-666, (1997)
  • [5] Ubertini F., Patch recovery based on complementary energy, International Journal for Numerical Methods in Engineering, 59, 11, pp. 1501-1538, (2004)
  • [6] Payen D.J., Bathe K.J., The use of nodal point forces to improve element stresses, Computers & Structures, 89, 5, pp. 485-495, (2011)
  • [7] Chen C., Structure Theory of Superconvergence of Finite Elements, pp. 29-37, (2002)
  • [8] Yuan S., Wang X., Xing Q., Et al., A scheme with optimal order of super-convergence based on EEP method: I formulation, Engineering Mechanics, 24, 10, pp. 1-5, (2007)
  • [9] Yuan S., Xing Q., Wang X., Et al., A scheme with optimal order of super-convergence based on EEP method: II Numerical results, Engineering Mechanics, 24, 11, pp. 1-6, (2007)
  • [10] Yuan S., Zhao Q., A scheme with optimal order of super-convergence based on EEP method: III Mathematical proof, Engineering Mechanics, 24, 12, (2007)
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