2-维Ginzburg-Landau方程的一种混合有限元方法的高精度分析  

Superconvergence Analysis of a Mixed Finite Element Method for Two-Dimension Ginzburg-Landau Equations

作　　者：李庆富 王俊俊 LI Qingfu;WANG Junjun(School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000,China)

机构地区：[1]平顶山学院数学与统计学院

出　　处：《应用数学》2019年第4期811-819,共9页Mathematica Applicata

基　　金：国家自然科学基金(11671369)

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.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.

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 

分 类 号：O242.21[理学—计算数学]