TY - JOUR
T1 - Residual-Based a Posteriori Estimators for the T/Ω Magnetodynamic Harmonic Formulation of the Maxwell System
AU - Creuse , E.
AU - Nicaise , S.
AU - Tang , Z.
AU - Menach , Y. L.
AU - Nemitz , N.
AU - Piriou , F.
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 411
EP - 429
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/575.html
KW - Maxwell equations, potential formulations, a posteriori estimators, finite element method.
AB - <p style="text-align: justify;">In this paper, we focus on an a posteriori residual-based error estimator for the $T/\Omega$ magnetodynamic harmonic formulation of the Maxwell system. Similarly to the $A/\varphi$ formulation
[7], the weak continuous and discrete formulations are established, and the well-posedness of
both of them is addressed. Some useful analytical tools are derived. Among them, an ad-hoc
Helmholtz decomposition for the $T/\Omega$ case is derived, which allows to pertinently split the error.
Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally
efficient. Finally, numerical tests confirm the theoretical results.</p>