Abstract：Several methods of a posteriori error estimation for finite element analysis are described, in which the explicit residual method, average method, and energy method are compared and analyzed in the computation of A- node-finite element analysis for eddy current fields. The expressions of a posteriori error estimation are proposed for the three methods used in adaptive finite element analysis. The numerical results of computational examples show that the residual method and average method can be applied to the a posteriori error estimation of eddy current loss calculation. If the emphasis is on the eddy current losses, the energy method does not be recommended.
李锦彪, 谢德馨. 三维稳态涡流场有限元分析的后验误差估计[J]. 电工技术学报, 2010, 25(4): 10-14.
Li Jinbiao, Xie Dexin. A Posteriori Error Estimation of Finite Element Analysis for Three Dimensional Steady State Eddy Current Fields. Transactions of China Electrotechnical Society, 2010, 25(4): 10-14.
[1] Penman J, Fraser J R. Dual and complementary energy methods in electromagnetism[J]. IEEE Transactions on Magnetics, 1983, 19(6): 2311-2316. [2] Mark Ainsworth, Tinsley Oden J. A posteriori error estimation in finite element analysis[M]. New York: A Wiley-Interscience Publication, 2000. [3] Beck R, Hiptmair R, Hoppe R, et al. Residual based a posteriori error estimators for eddy current computation[J]. M2AN, 2000, 34(1): 159-182. [4] Zienkiewicz O C, Taylor R L. The finite element method[M]. New York: Butterworth-Heinemann, 2005. [5] Yamazaki K, Watari S, Egawa A. Adaptive finite element meshing for eddy current analysis of moving conductor[J]. IEEE Transactions on Magnetics, 2004, 40(2): 993-996. [6] Golias N A, Tsiboukis T D. 3-D eddy-current computation with a self-adaptive refinement technique[J]. IEEE Transactions on Magnetics, 1995, 31(3): 2261-2268. [7] Krebs G, Abakar A, Clenet S. Comparison of error estimators in eddy current testing[J]. IEEE Transactions on Magnetics, 2009, 45(3): 968-971. [8] Ladas D, Mazauric V, Meunier G, et al. An energy based approach of electromagnetism applied to adaptive meshing and error criteria[J]. IEEE Transactions on Magnetics, 2008, 44(6): 1246-1249. [9] 程志光, 高桥则雄, 博扎德·弗甘尼, 等. 电气工程电磁热场模拟与应用[M]. 北京: 科学出版社, 2009. [10] 谢德馨, 姚缨英, 白保东, 等. 三维涡流场的有限元分析[M]. 北京: 机械工业出版社, 2007.
2010, Vol. 25 
