UNCONDITIONAL SUPERCONVERGENCE ANALYSIS OF AN H1-GALERKIN MIXED FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL GINZBURG-LANDAU EQUATION

• 来源期刊: 计算数学（英文版）
• 关键词: The two-dimensional Ginzburg-Landau equation H1-Galerkin MFEM Temporal and spatial errors Unconditionally Superconvergent results
• 年，卷（期）: 2019,（4）
• 页码范围: 437-457
• 页数: 21页
• 语种: 英文
• DOI: 10.4208/jcm.1802-m2017-0198

摘要

An H1-Galerkin mixed finite element method (MFEM) is discussed for the two-dimensional Ginzburg-Landau equation with the bilinear element and zero order Raviart-Thomas element (Q11 + Q10 × Q01).A linearized Crank-Nicolson fully-discrete scheme is developed and a time-discrete system is introduced to split the error into two parts which are called the temporal error and the spatial error,respectively.On one hand,the regularity of the time-discrete system is deduced through the temporal error estimation.On the other hand,the superconvergent estimates of u in H1-norm and (q) in H(div;Ω)-norm with order O(h2 + τ2) are obtained unconditionally based on the achievement of the spatial result.At last,a numerical experiment is included to illustrate the feasibility of the proposed method.Here,h is the subdivision parameter and τ is the time step.