title: Convergence of finite element approximations and multilevel linearization for Ginzburg-Landau model of d-wave superconductors
abstract: In this paper, we consider the finite element approximations of a recently proposed Ginzburg-Landau-type model for d-wave superconductors. In contrast to the conventional Ginzburg-Landau model the scalar complex valued order-parameter is replaced by a multicomponent complex order-parameter and the free energy is modified according to the d-wave paring symmetry. Convergence and optimal error estimates and some super-convergent estimates for the derivatives are derived. Furthermore, we propose a multilevel linearization procedure to solve the nonlinear systems. It is proved that the optimal error estimates and super-convergence for the derivatives are preserved by the multi-level linearization algorithm
keyphrases: multilevel linearization Ginzburg-Landau model d-wave free energy error estimation nonlinear systems superconductivity finite element method two-grid method