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\begin{equation*} \begin {cases} \nabla \times \left (\sigma ^{-1}(\mathbf {x} )\nabla \times \mathbf {E}(\mathbf {x} )\right )&=~ \epsilon (\mathbf {x} ) \mathbf {u}(\mathbf {x}), \quad \mathbf {x} \in \Omega \\ \nabla \cdot (\epsilon (\mathbf {x} ) \mathbf {E}(\mathbf {x} )) &=~ \rho (\mathbf {x} ), \quad \phantom {xxxi} \mathbf {x} \in \Omega \\ \mathbf {E}(\mathbf {x} )\times \vec {\mathbf {n}}(\mathbf {x}) &=~ \mathbf {0}, \quad \phantom {xxxxxx} \mathbf {x} \in \partial \Omega \\ \nabla \cdot \left ( \epsilon (\mathbf {x} ) \mathbf {u}(\mathbf {x})\right ) &=~0, \quad \phantom {xxxxxx}\mathbf {x} \in \Omega \end{cases} \end{equation*}
with the Nédélec finite elements. We show the convergence of the finite element approximations as well as establish their error bounds.