Analyses, algorithms, and computations for models of high-temperature superconductivity. Final report

Under the sponsorship of the Department of Energy, the authors have achieved significant progress in the modeling, analysis, and computation of superconducting phenomena. The work so far has focused on mezoscale models as typified by the celebrated Ginzburg-Landau equations; these models are intermediate between the microscopic models (that can be used to understand the basic structure of superconductors and of the atomic and sub-atomic behavior of these materials) and the macroscale, or homogenized, models (that can be of use for the design of devices). The models they have considered include a time dependent Ginzburg-Landau model, a variable thickness thin film model, models for high values of the Ginzburg-landau parameter, models that account for normal inclusions and fluctuations and Josephson effects, and the anisotropic ginzburg-Landau and Lawrence-Doniach models for layered superconductors, including those with high critical temperatures. In each case, they have developed or refined the models, derived rigorous mathematical results that enhance the state of understanding of the models and their solutions, and developed, analyzed, and implemented finite element algorithms for the approximate solution of the model equations