## Preprint 2011-20

## Rodolfo Rodríguez, Pablo Venegas:

### Numerical approximation of the spectrum of the curl operator

### Abstract:

The aim of this paper is to study the numerical approximation of the eigenvalue problem for the curl operator. The three-dimensional divergence-free eigensolutions of this problem are examples of the so-called Beltrami fields or linear force-free fields, which arise in various physics areas such as solar physics, plasma physics, and fluid mechanics. The present analysis is restricted to bounded simply-connected domains. A finite element discretization of a convenient weak formulation of the spectral problem is proposed and analyzed. Optimal-order spectral convergence is proved, as well as absence of spurious modes. The results of some numerical tests are also reported.