The aim of this paper is to propose and analyze a numerical method to solve transient eddy current problems formulated in terms of the magnetic field intensity. Space discretization is based on Nédélec edge elements, while a backward Euler scheme is used for time discretization; the curl-free constraint in the dielectric domain is imposed by means of a penalty strategy. Convergence of the penalized problem as the penalty parameter goes to zero is proved for the continuous and the discrete problems, for the latter uniformly in the discretization parameters. Optimal order error estimates for the convergence of the discrete penalized problem with respect to the penalty and the discretization parameters are also proved. Finally, some numerical tests are reported to assess the performance of this approach.

本文的目的是提出并分析一种数值方法，以解决根据磁场强度制定的瞬态涡流问题。空间离散化基于Nédélec边缘元素，而后向Euler方案用于时间离散化；介电域中的无卷曲约束是通过惩罚策略施加的。对于连续问题和离散问题，证明了惩罚问题随着惩罚参数趋于零而收敛，对于离散问题，后者是一致的。还证明了针对罚分和离散化参数收敛的离散惩罚问题收敛的最优阶误差估计。最后，报告了一些数值测试以评估这种方法的性能。