Goal-oriented error estimation based on equilibrated flux reconstruction for the approximation of the harmonic formulations in eddy current problems - Laboratoire de Matériaux Céramiques et de Mathématiques - Ceramaths Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

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 − φ) formulation arising in the modeling of eddy current problems, approximated by nonconforming finite element methods. It is based on the resolution of a dual 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 reminder 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)

Identifiants

  • HAL Id : hal-03954215 , version 1

Citer

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. 2023. ⟨hal-03954215v1⟩
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