## Preprint 2011-08

## Alfredo Bermúdez, Rafael Muñoz-Sola, Carlos Reales, Rodolfo Rodríguez, Pilar Salgado:

### Mathematical and numerical analysis of a transient eddy current problem arising from electromagnetic forming

### Abstract:

Electromagnetic forming is a type of high velocity cold forming process for electrically conductive metals. The aim of this paper is to introduce and analyze a weak formulation of the underlying transient axisymmetric eddy current problem governing such phenomenon. The resulting problem is degenerate parabolic with the time derivative acting on a moving subdomain. Because of this, we have to resort to regularization arguments in order to prove its well-posedness. We propose a finite element method in space combined with a backward Euler time scheme for its numerical solution. We obtain error estimates and report numerical results which allow us to assess the performance of the proposed method.

This preprint gave rise to the following definitive publication(s):

**Alfredo BERMúDEZ, Rafael MUñOZ-SOLA, Carlos REALES, Rodolfo RODRíGUEZ, Pilar SALGADO: ***Mathematical and numerical analysis of a transient eddy current problem arising from electromagnetic forming*. SIAM Journal on Mathematical Analysis, vol. 45, 6, pp. 3629-3650, (2013)