Dra. Camaño-Valenzuela, Jessika

We construct sets of basis functions of the space of divergence-free finite elements of Raviart–Thomas type in domains of general topology. Two different methods are presented: one using a suitable selection of the curls of Nédélec finite elements, the other based on an efficient algebraic procedure. The first approach looks to be more useful for numerical approximation, as the basis functions have a localized support.

In the published article, Figure 5 corresponds to an eigenfunction associated not with the first smallest positive eigenvalue. A correct eigenfunction of the latter is depicted in Fig. 1 here. Note that this eigenfunction is axisymmetric, as can be seen from Fig. 2 where its radial, azimuthal and vertical components are plotted on different meridian sections.