A Posteriori Error Estimation of Finite Element Solutions via the Direct Use of Higher Order Hierarchal Test Functions

[en] An a posteriori error estimation of finite element solutions based on the lack of fulfillment of weak formulations is developed and applied to low frequency electromagnetic problems. The error is quantified via higher order hierarchal test functions and local computations of their contributions on the solutions. The method only uses the weak formulation under study with no need of other kind of evaluation.

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)

Language :

English

Title :

A Posteriori Error Estimation of Finite Element Solutions via the Direct Use of Higher Order Hierarchal Test Functions

Publication date :

March 2009

Journal title :

IEEE Transactions on Magnetics

ISSN :

0018-9464

eISSN :

1941-0069

Publisher :

IEEE, Piscataway, United States - New Jersey

Volume :

Issue :

Pages :

1360-1363

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 04 February 2011

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Bibliography

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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.
L. Janicke and A.Kost, "Error estimation and adaptive mesh generation in the 2D and 3D finite element method," IEEE Trans. Magn., vol. 32, no. 3, pp. 1334-1337, 1996.
J. A. H. Rikabi, C. F. Bryant, and E. M. Freeman, "Complementary solutions of electrostatic field problems," IEEE Trans. Magn., vol. 25, no. 6, pp. 4427-4442, 1989.
J. F. Remacle, P. Dular, F. Henrotte, A. Genon, and W. Legros, "Error estimation and mesh optimisation using error in constitutive relation for electromagnetic field computation," IEEE Trans. Magn., vol. 31, no. 6, pp. 3587-3589, 1995.
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P. Dular, J. Gyselinck, T. Henneron, and F. Piriou, "Dual finite element formulations for lumped reluctances coupling," IEEE Trans. Magn., vol. 41, no. 5, pp. 1396-1399, 2005.

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