document: Convergence of finite element approximations and multilevel linearization for Ginzburg-Landau model of d-wave superconductors 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
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