2-维Ginzburg-Landau方程H^1-Galerkin有限元方法的高精度分析  

Superconvergence Analysis of an H^1-Galerkin Mixed Finite Element Method for Two-dimension Ginzburg-Landau Equations

作　　者：赵明霞 李庆富 石东洋 ZHAO Mingxia;LI Qingfu;SHI Dongyang(School of Mathematics and Statistics,Pingdingshan University,Pingdingshan 467000,China;School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]平顶山学院数学与统计学院,河南平顶山467000 [2]郑州大学数学与统计学院,河南郑州450001

出　　处：《信阳师范学院学报（自然科学版）》2019年第1期17-22,共6页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11271340)

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.EQ^rot1 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.

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 

分 类 号：O242.21[理学—计算数学]