## Preprint 2019-11

## Alfredo Bermúdez, Bibiana López-Rodríguez, Rodolfo Rodríguez, Pilar Salgado:

### Numerical analysis of a penalty approach for the solution of a transient eddy current problem

### Abstract:

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 Nedelecc 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.

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

**Alfredo BERMúDEZ, Bibiana LóPEZ-RODRíGUEZ, Rodolfo RODRíGUEZ, Pilar SALGADO: ***Numerical analysis of a penalty approach for the solution of a transient eddy current problem*. Computers & Mathematics with Applications, vol. 79, pp. 2503-2526 (2020).