Convergence of Finite Element Approximations and Multilevel Linearization for Ginzburg–Landau Model of d-Wave Superconductors |
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Authors: | Huang Yunqing Xue Weimin |
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Institution: | (1) Department of Mathematics, Xiangtan University, 411105, P.R. China;(2) Department of mathematics, Hong Kong Baptist University, Kowloon, Hong Kong |
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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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Keywords: | Ginzburg– Landau model d-wave superconductivity finite element error estimates two-grid method multilevel linearization |
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