Eddy currents; error estimation; finite element method
Abstract :
[en] The finite element computation of eddy current problems introduces numerical error. This error can only be estimated. Among all error estimators (EEs) already developed, two estimators, called residual and hierarchical EEs, proven to be reliable and efficient, are theoretically and numerically compared. Both estimators show similar behaviors and locations of the error.
Research Center/Unit :
Applied and computational electromagnetics
Disciplines :
Electrical & electronics engineering
Author, co-author :
Dular, Patrick ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Tang, Zuqi; Université Lille 1 > Laboratoire Paul Painlevé, L2EP
Le Ménach, Yvonnick; Université Lille 1 > L2EP
Creusé, Emmanuel; Université Lille 1 > Laboratoire Paul Painlevé
Piriou, Francis; Université Lille 1 > L2EP
Language :
English
Title :
Comparison of Residual and Hierarchical Finite Element Error Estimators in Eddy Current Problems
I. Babuska and W. C. Rheinboldt, "A-posteriori error estimates for the finite element method," Int. J. Numer. Methods Eng., vol. 12, no. 10, pp. 1597-1615, 1978.
R. Beck, R. Hiptmair, R. H. W. Hoppe, and B. Wohlmuth, "Residual based a posteriori error estimators for eddy current computation," ESAIM, Math. Model. Numer. Anal., vol. 34, no. 1, pp. 159-182, 2000.
J. Chen, Z. Chen, T. Cui, and L. B. Zhang, "An adaptive finite element method for the eddy current model with circuit/field couplings," SIAM J. Sci. Comput., vol. 32, no. 2, pp. 1020-1042, 2010.
E. Creusé, S. Nicaise, Z. Tang, Y. Le Menach, N. Nemitz, and F. Piriou, "Residual-based a posteriori estimators for the A magnetodynamic harmonic formulation of the Maxwell system," Math. Models Methods Appl. Sci., vol. 22, no. 5, pp. 1-31, 2012.
P. Dular, "A posteriori error estimation of finite element solutions via the direct use of higher order hierarchal test functions," IEEE Trans. Magn., vol. 45, no. 3, pp. 1360-1363, Mar. 2009.
J. P. Webb and B. Forghani, "Hierarchal scalar and vector tetrahedra," IEEE Trans. Magn., vol. 29, no. 2, pp. 1495-1498, Mar. 1993.
R. E. Bank and R. K. Smith, "A posteriori error estimates based on hierarchical bases," SIAM J. Numer. Anal., vol. 30, no. 4, pp. 921-935, 1993. (Pubitemid 23696966)
