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

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Creusé, Emmanuel | Nicaise, Serge | Tang, Zuqi

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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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