Abstract The aim of this article is to analyze a transient axisymmetric electromagnetic model involving velocity terms in the Ohm's law. To this end, we introduce a time‐dependent weak formulation leading to a degenerate parabolic problem and establish its well posedness.We propose a finite‐element method for space discretization and prove well posedness and error estimates. Then, we combine it with a backward Euler time discretization and prove stability and error estimates. Finally, numerical results assessing the performance of the method are reported. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011