| 2-维Ginzburg-Landau方程H~1-Galerkin有限元方法的高精度分析 |
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| 引用本文： | 赵明霞,李庆富,石东洋.2-维Ginzburg-Landau方程H~1-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(1):17-22. |
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| 作者姓名： | 赵明霞 李庆富 石东洋 |
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| 作者单位： | 平顶山学院数学与统计学院;郑州大学数学与统计学院 |
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| 摘 要： | 采用非协调单元EQ~(rot)_1及零阶Raviart-Thomas元(EQ~(rot)_1+Q_(10)×Q_(01)),对2-维Ginzburg-Landau方程讨论了一种H~1-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H~1模意义下及流量■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.
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| 关 键 词： | Ginzburg-Landau方程 H~1-Galerkin混合有限元方法 半离散格式 线性化的Euler全离散格式 超逼近性质 |
Superconvergence Analysis of an H~1-Galerkin Mixed Finite Element Method for Two-dimension Ginzburg-Landau Equations |
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| Institution: | ,School of Mathematics and Statistics,Pingdingshan University,School of Mathematics and Statistics,Zhengzhou University |
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| Abstract: | EQ_1~(rot)nonconforming finite element and zero order Raviart-Thomas element are applied to discuss an H~1-Galerkin mixed finite element method( MFEM) for the two-dimension Ginzburg-Landau equations. The superclose results of original variant u in H~1-norm and flux variant H( div; Ω) in L~2-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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| Keywords: | Ginzburg-Landau equations H~1-Galerkin MFEM semi-discrete scheme linearized Euler fully-discrete scheme superclose properties |
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