Performance of the Adaptive Finite Element Method Based on the Element-Energy-Projection Technique

被引：0
|
作者：
Sun H.-H. [1 ]
Yuan S. [1 ]
机构：
[1] Department of Civil Engineering, Tsinghua University, Beijing
来源：
Gongcheng Lixue/Engineering Mechanics | 2019年 / 36卷 / 02期
关键词：
Adaptive procedure; EEP; FEM; Optimum mesh; SPR; Super-convergence;
D O I：
10.6052/j.issn.1000-4750.2018.10.0439
中图分类号：
学科分类号：
摘要：
The adaptive finite element method (AFEM) based on the element energy projection (EEP) technique has succeeded in solving a wide range of problems, while few studies have been done on its adaptive characteristics. Taking the second-order ordinary differential equation as the model problem, the adaptive methods based on both the EEP and super-convergent patch recovery (SPR) solutions were studied. The meshes generated by the two adaptive methods were compared with the optimum mesh. Furthermore, an estimate formula reflecting the characteristics of AFEM was proposed with an adaptive convergence rate β. Numerical experiments show that, with the element of degree m, both SPR and EEP can be well applied for the smooth problem and the convergence rate achieved m+1. For the singular problem with a singularity factor α(<1), SPR failed while EEP-based adaptive procedure gained the convergence rate of m+α, a much higher rate than that of the conventional finite element method α. © 2019, Engineering Mechanics Press. All right reserved.
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页码：17 / 25
页数：8
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共 27 条
  • [1] Nochetto R.H., Veeser A., Primer of Adaptive Finite Element Methods, Multiscale and Adaptivity: Modeling, Numerics and Applications, pp. 125-225, (2011)
  • [2] Cascon J.M., Kreuzer C., Nochetto R.H., Et al., Quasi-optimal convergence rate for an adaptive finite element method, SIAM Journal on Numerical Analysis, 46, 5, pp. 2524-2550, (2008)
  • [3] Chen L., Zhang C.S., AFEM@ Matlab: A Matlab package of adaptive finite element methods, (2006)
  • [4] Zienkiewicz O.C., Zhu J.Z., A simple error estimator and adaptive procedure for practical engineerng analysis, International Journal For Numerical Methods in Engineering, 24, 2, pp. 337-357, (1987)
  • [5] 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)
  • [6] Zienkiewicz O.C., Zhu J.Z., The superconvergent patch recovery and a posteriori error estimates. Part 2: Error Estimates and Adaptivity, International Journal for Numerical Methods in Engineering, 33, 7, pp. 1365-1382, (1992)
  • [7] Zienkiewicz O.C., Zhu J.Z., The superconvergent patch recovery (SPR) and adaptive finite element refinement, Computer Methods in Applied Mechanics and Engineering, 101, 1-3, pp. 207-224, (1992)
  • [8] Wiberg N.E., Li X.D., Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate, International Journal for Numerical Methods in Biomedical Engineering, 10, 4, pp. 313-320, (1994)
  • [9] Wiberg N.E., Abdulwahab F., Li X.D., Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) techniques, Archives of Computational Methods in Engineering, 4, 3, pp. 203-242, (1997)
  • [10] Creuse E., Nicaise S., A posteriori error estimator based on gradient recovery by averaging for discontinuous Galerkin methods, Journal of Computational and Applied Mathematics, 234, 10, pp. 2903-2915, (2010)
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