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赵明霞, 李庆富, 石东洋. 2-维Ginzburg-Landau方程H1-Galerkin有限元方法的高精度分析[J]. 信阳师范学院学报(自然科学版), 2019, 32(1): 17-22. DOI: 10.3969/j.issn.1003-0972.2019.01.004
引用本文: 赵明霞, 李庆富, 石东洋. 2-维Ginzburg-Landau方程H1-Galerkin有限元方法的高精度分析[J]. 信阳师范学院学报(自然科学版), 2019, 32(1): 17-22. DOI: 10.3969/j.issn.1003-0972.2019.01.004
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ZHAO Mingxia, LI Qingfu, SHI Dongyang. Superconvergence Analysis of an H1-Galerkin Mixed Finite Element Method for Two-dimension Ginzburg-Landau Equations[J]. Journal of Xinyang Normal University (Natural Science Edition), 2019, 32(1): 17-22. DOI: 10.3969/j.issn.1003-0972.2019.01.004
Citation: ZHAO Mingxia, LI Qingfu, SHI Dongyang. Superconvergence Analysis of an H1-Galerkin Mixed Finite Element Method for Two-dimension Ginzburg-Landau Equations[J]. Journal of Xinyang Normal University (Natural Science Edition), 2019, 32(1): 17-22. DOI: 10.3969/j.issn.1003-0972.2019.01.004
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2-维Ginzburg-Landau方程H1-Galerkin有限元方法的高精度分析

Superconvergence Analysis of an H1-Galerkin Mixed Finite Element Method for Two-dimension Ginzburg-Landau Equations

    摘要
  • 摘要: 采用非协调单元EQ1rot及零阶Raviart-Thomas元（EQ1rot+Q10×Q01），对2-维Ginzburg-Landau方程讨论了一种H1-Galerkin混合有限元方法.在半离散和线性化Euler全离散格式下，分别有技巧地导出了原始变量u在H1模意义下及流量p在H（div；Ω）模意义下的超逼近性质.最后，给出两个数值算例验证了理论结果.

     

    Abstract: EQ1rot nonconforming finite element and zero order Raviart-Thomas element are applied to discuss an H1-Galerkin mixed finite element method(MFEM) for the two-dimension Ginzburg-Landau equations. The superclose results of original variant u in H1-norm and flux variant H(div;Ω) in L2-norm are derived technically under the semi-discrete scheme and the linearized Euler fully-discrete scheme. At last, numerical experiment is included to illustrate the feasibility of the proposed method.

     

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