2-维Ginzburg-Landau方程<i>H</i><sup>1</sup>-Galerkin有限元方法的高精度分析

2-维Ginzburg-Landau方程H¹-Galerkin有限元方法的高精度分析

摘要: 采用非协调单元EQ₁^rot及零阶Raviart-Thomas元（EQ₁^rot+Q₁₀×Q₀₁），对2-维Ginzburg-Landau方程讨论了一种H¹-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H¹模意义下及流量p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.

Abstract: EQ₁^rot nonconforming finite element and zero order Raviart-Thomas element are applied to discuss an H¹-Galerkin mixed finite element method(MFEM) for the two-dimension Ginzburg-Landau equations. The superclose results of original variant u in H¹-norm and flux variant H(div;Ω) in L²-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.