Convergence analysis of a numerical method for a mean field model of superconducting vortices

In the mean field models of superconductivity, the individual vortex-like structures occurring in practical type-II superconductors are averaged and a vortex density is solved for them. The numerical solution of the mean field models makes large-scale simulations of vortex phenomena possible. In this paper, we present a simple convergence analysis for a numerical method based on hybrid finite element/finite volume/finite difference approximations in the two-dimensional case, by providing various different interpretations to the discretization scheme.