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Analysis and Convergence of a Covolume Approximation of the Ginzburg--Landau Model of Superconductivity

In this paper, we present the mathematical analysis of a covolume method for the approximations of the Ginzburg--Landau (GL) model for superconductivity. A nice feature of this approach is that the gauge invariance properties are retained in discrete approximations based on triangular grids. We also use properties of discrete vector fields to study issues such as the gauge choices and their enforcement.