Superconducting axisymmetric finite elements based on a gauged potential variational principle—I. Formulation

The present work is part of a research program for the numerical simulation of electromagnetic (EM) fields within conventional Ginzburg-Landau (GL) superconductors. The final goal of this research is to formulate, develop and validate finite element (FE) models that can accurately capture electromagnetic, thermal and material phase changes in a superconductor. The formulations presented here are for a time-independent Ginzburg-Landau superconductor and are derived from a potential-based variational principle.