A guaranteed equilibrated error estimator for the $\mathbf{A}-\varphi$ and $\mathbf{T}-\Omega$ magnetodynamic harmonic formulations of the Maxwell system
Résumé
In this paper, a guaranteed equilibrated error estimator is proposed for the harmonic magnetodynamic formulation of the Maxwell's system. This system is recast in two classical potential formulations, which are solved by a Finite Element method. The equilibrated estimator is built starting from these dual problems and is consequently available to estimate the error of both numerical resolutions. The estimator reliability and efficiency without generic constants are established. Then, numerical tests are performed, allowing to illustrate the obtained theoretical results.
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