Simplified models of superconducting-normal-superconducting junctions and their numerical approximations

When a thin layer of normal (non-superconducting) material is placed betwee n layers of superconducting material, a superconducting-normal-superconduct ing junction is formed. This paper considers a model for the junction based on the Ginzburg-Landau equations as the thickness of the normal layer tend s to zero, The model is first derived formally by averaging the unknown var iables in the normal layer. Rigorous convergence is then established, as we ll as an estimate for the order of convergence. Numerical results are shown for one-dimensional junctions.