Details of Research Outputs

The paper focuses on analysis of linearized Galerkin FEMs for a mixed formulation of the time-dependent Ginzburg–Landau equations under the temporal gauge. We provide optimal error estimates in L²-norm for the order parameter ?_h and the magnetic field s_h unconditionally, although the accuracy of the numerical magnetic potential A_h is one-order lower than the optimal one due to the degeneracy of the magnetic potential equation. Since the states of superconductors are determined by the order parameter ?_h (or the density of the superconducting electron pairs |?_h|), the accuracy of ?_h is more important for the vortex simulation in superconditors. Our analysis is based on a nonclassical Ritz projection, which may reduce the pollution of inaccuracy of the numerical magnetic potential in analysis. Numerical experiments confirm our theoretical analysis. © 2018 Society for Industrial and Applied Mathematics.