| 2-维Ginzburg-Landau方程的一种混合有限元方法的高精度分析 |
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| 引用本文： | 李庆富 王俊俊. 2-维Ginzburg-Landau方程的一种混合有限元方法的高精度分析[J]. 应用数学, 2019, 32(4): 811-819 |
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| 作者姓名： | 李庆富 王俊俊 |
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| 作者单位： | 平顶山学院数学与统计学院, 河南 平顶山 467000 |
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| 基金项目： | 国家自然科学基金(11671369) |
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| 摘 要： | 针对2-维Ginzburg-Landau方程,采用EQ1^ rot非协调元及零阶Raviart-Thomas元讨论了一种混合有限元方法.在半离散格式和线性化的Euler格式下,分别有技巧的导出了原始变量u在H^ 1能量模意义下及流量p^→在L^2模意义下的O (h^2 +τ^2 )阶的超逼近性质.给出一个数值算例验证了理论结果的正确性.
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| 关 键 词： | 2-维Ginzburg-Landau方程 混合有限元方法 半离散格式 线性化的二阶全离散格式 超逼近结果 |
Superconvergence Analysis of a Mixed Finite Element Method for Two-Dimension Ginzburg-Landau Equations |
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| LI Qingfu,WANG Junjun. Superconvergence Analysis of a Mixed Finite Element Method for Two-Dimension Ginzburg-Landau Equations[J]. Mathematica Applicata, 2019, 32(4): 811-819 |
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| Authors: | LI Qingfu WANG Junjun |
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| Affiliation: | (School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000,China) |
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| Abstract: | E Q1^ rot nite element and zero order Raviart-Thomas element are applied to discuss a kind of mixed nite element method(MFEM) for the two-dimension Ginzburg-Landau equations. The superclose results of original variant u in H ^1 -norm and ux variant H (div;Ω) in L2 -norm with O(h^2 +τ^2 ) 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: | Two-dimension Ginzburg-Landau equation MFEM Semi-discrete scheme Linearized second-order fully-discrete scheme Superclose property |
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