Space-Time Residual-Based A Posteriori Estimators for the
A−ϕ Magnetodynamic Formulation of the Maxwell System

Creusé, Emmanuel; Nicaise, Serge; Tittarelli, Roberta

doi:10.1515/cmam-2014-0015

Cited by 6 publications

(7 citation statements)

References 31 publications

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“…In conclusion, the reliability and efficiency's properties lead to deduce the equivalence between the estimator and a suitable error energy norm [3].…”

Section: B Efficiencymentioning

confidence: 96%

“…For each of them, the proof of their well-posedness and some properties on the corresponding solutions are detailed in [3,Sec. 2].…”

Section: B Potential Weak Formulationsmentioning

confidence: 99%

“…In the following, h T and h F represent, respectively, the diameter of the element T and of the face F. Let X 0 h ( ) and h ( c ) be the FE approximation spaces, respectively, for X 0 ( ) and H 1 ( c ). In particular, A m is approximated by first-order edge elements and ϕ m by first-order nodal elements, as better specified in [3,Sec. 2.3].…”

Section: B Potential Weak Formulationsmentioning

confidence: 99%

“…In [3], we have proven the upper bound for the global in space and in time error, corresponding to the reliability property of the estimator…”

Section: B Potential Weak Formulationsmentioning

confidence: 99%

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Space-Time Residual-Based <italic>a posteriori</italic> Estimator for the <inline-formula> <tex-math notation="LaTeX">$A-\varphi$ </tex-math></inline-formula> Formulation in Eddy Current Problems

Tittarelli¹,

Menach²,

Creusé³

et al. 2015

IEEE Trans. Magn.

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In this paper, an a posteriori residual error estimator is presented for the 3-D eddy current problem modeled by the space-time A − ϕ potential formulation. It is solved by the finite element method in space and the backward Euler scheme in time. Once the reliability as well as the efficiency of the estimator is established, two numerical tests are proposed: 1) an analytical one to validate the theoretical results and 2) a physical one to illustrate the performance for a real eddy current problem.Index Terms-Eddy current, finite element (FE) analysis, potential formulation, space-time a posteriori estimators.

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“…In conclusion, the reliability and efficiency's properties lead to deduce the equivalence between the estimator and a suitable error energy norm [3].…”

Section: B Efficiencymentioning

confidence: 96%

“…For each of them, the proof of their well-posedness and some properties on the corresponding solutions are detailed in [3,Sec. 2].…”

Section: B Potential Weak Formulationsmentioning

confidence: 99%

Section: B Potential Weak Formulationsmentioning

confidence: 99%

“…In [3], we have proven the upper bound for the global in space and in time error, corresponding to the reliability property of the estimator…”

Section: B Potential Weak Formulationsmentioning

confidence: 99%

See 2 more Smart Citations

Space-Time Residual-Based <italic>a posteriori</italic> Estimator for the <inline-formula> <tex-math notation="LaTeX">$A-\varphi$ </tex-math></inline-formula> Formulation in Eddy Current Problems

Tittarelli¹,

Menach²,

Creusé³

et al. 2015

IEEE Trans. Magn.

Self Cite

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“…More particularly, we have in mind to derive a weak formulation that will be used for the numerical resolution of (8) by the Finite Element Method in the context of electromagnetic problems. [4] Concerning the harmonic formulation of some Maxwell problems, several contributions have been proposed in the last decade. In that case, since no time derivatives are involved, we have only to deal with spatial problems for which existence results are easier to obtain (see for instance Theorem 2.1 in [5]).…”

Section: Introductionmentioning

confidence: 99%

Existence results for the A & φ magnetodynamic formulation of the Maxwell system

Nicaise

2014

Applicable Analysis

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Robust model order reduction of an electrical machine at startup through reduction error estimation

Montier

Henneron

Clénet

et al. 2017

Int J Numerical Modelling

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In the field of electrical machines, the finite element method provides accurate results but requires a high computational cost to perform, with sometimes weeks of computations. Therefore, model order reduction methods such as the proper orthogonal decomposition combined with the discrete empirical interpolation method are able to speed up the solution of the finite element problem. To use the obtained results for predictive computations, an error estimator is required.However, the different estimators found in the literature do not apply to our problem. Therefore, a simple error indicator that can be applied to a wide range of problems is proposed in this paper. KEYWORDS discrete empirical interpolation method, electrical machine, error estimation, finite element method, model order reduction, proper orthogonal decomposition Int J Numer Model. 2018;31:e2277.wileyonlinelibrary.com/journal/jnm

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Space-Time Residual-Based A Posteriori Estimators for the A−ϕ Magnetodynamic Formulation of the Maxwell System

Cited by 6 publications

References 31 publications

Space-Time Residual-Based <italic>a posteriori</italic> Estimator for the <inline-formula> <tex-math notation="LaTeX">$A-\varphi$ </tex-math></inline-formula> Formulation in Eddy Current Problems

Space-Time Residual-Based <italic>a posteriori</italic> Estimator for the <inline-formula> <tex-math notation="LaTeX">$A-\varphi$ </tex-math></inline-formula> Formulation in Eddy Current Problems

Existence results for the A & φ magnetodynamic formulation of the Maxwell system

Robust model order reduction of an electrical machine at startup through reduction error estimation

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