A new error analysis of backward Euler Galerkin finite element method for two-dimensional time-dependent Ginzburg-Landau equation

被引：1
|
作者：
Yang, Huaijun [1 ]
机构：
[1] Zhengzhou Univ Aeronaut, Sch Math, Zhengzhou 450046, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2023年 / 145卷
基金：
中国国家自然科学基金;
关键词：
Time-dependent Ginzburg-Landau equation; Backward Euler Galerkin FEM; Unconditionally optimalL2 error estimate; UNCONDITIONAL SUPERCONVERGENT ANALYSIS;
D O I：
10.1016/j.aml.2023.108767
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the backward Euler Galerkin finite element method (FEM) is investigated for the two dimensional time-dependent Ginzburg-Landau equation. The unconditionally optimal L2 error estimate is obtained without using the boundedness of the numerical solution in L & INFIN; norm, while it is an indispensable requirement in the previous works. A key to the analysis is to deal with the nonlinear term rigorously and skillfully in terms of the boundedness of the numerical solution in L2 norm rather than the L & INFIN; norm. Numerical results are presented to confirm the theoretical findings.& COPY; 2023 Elsevier Ltd. All rights reserved.
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