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Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2024

Goal-oriented error estimation based on equilibrated flux reconstruction for the approximation of the harmonic formulations in eddy current problems

Résumé

In this work, we propose an a posteriori goal-oriented error estimator for the harmonic A/Phi formulation arising in the modeling of eddy current problems, approximated by nonconforming finite element methods. It is based on the resolution of an adjoint problem associated with the initial one. For each of these two problems, a guaranteed equilibrated estimator is developed using some flux reconstructions. These fluxes also allow to obtain a goal-oriented error estimator that is fully computable and can be split in a principal part and a remainder one. Our theoretical results are illustrated by numerical experiments.
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Dates et versions

hal-03954215 , version 1 (24-01-2023)
hal-03954215 , version 2 (30-01-2024)

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Emmanuel Creusé, Serge Nicaise, Zuqi Tang. Goal-oriented error estimation based on equilibrated flux reconstruction for the approximation of the harmonic formulations in eddy current problems. IMA Journal of Numerical Analysis, 2024, ⟨10.1093/imanum/drad107⟩. ⟨hal-03954215v2⟩
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