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Convergence of Finite Element Approximations and Multilevel Linearization for Ginzburg–Landau Model of d-Wave Superconductors

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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 superconvergent 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 superconvergence for the derivatives are preserved by the multilevel linearization algorithm.

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Authors and Affiliations

  1. Department of Mathematics, Xiangtan University, 411105, P.R. China

    Yunqing Huang

  2. Department of mathematics, Hong Kong Baptist University, Kowloon, Hong Kong

    Weimin Xue

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  1. Yunqing Huang
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  2. Weimin Xue
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Huang, Y., Xue, W. Convergence of Finite Element Approximations and Multilevel Linearization for Ginzburg–Landau Model of d-Wave Superconductors. Advances in Computational Mathematics 17, 309–330 (2002). https://doi.org/10.1023/A:1016293508648

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