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

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.