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We develop an adaptive finite element method for solving the eddy current model with voltage excitations for complicated three-dimensional structures. The mathematical model is based on the A-φ formulation whose well-posedness is established. We derive the a posteriori error estimate for the finite element approximation of the model whose solution is not unique in the nonconducting region. Numerical experiments that illustrate the competitive behavior of the proposed method are provided.
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Chen et al. (2010) studied this question.
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