A time discrete scheme for an electromagnetic contact problem with moving conductor

摘要

In the context of multi-component electromagnetic problems, we investigate an eddy current model with moving conductor. The time derivative acting on the moving subdomain and the jumps of the material coefficients on the interfaces raise the challenge to handle the boundary term which is gained by the Reynolds transport theorem. A time-discrete scheme based on backward Euler’s method is proposed to solve this problem. Using Rothe’s method, we show the stability as well as the convergence to a unique weak solution of the variational system.