@Article{JCM-37-4,
author = {Shi, Dongyang and Wang, Junjun},
title = {Unconditional Superconvergence Analysis of an $H^1$-Galerkin Mixed Finite Element Method for Two-Dimensional Ginzburg-Landau Equation},
journal = {Journal of Computational Mathematics},
year = {2019},
volume = {37},
number = {4},
pages = {437--457},
abstract = {<p style="text-align: justify;">An $H^1$-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 $(Q_{11} + Q_{10} × Q_{01})$. 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 $H^1$-norm and $\vec{q}$ in $H$(div; Ω)-norm with order $O(h^2 + τ^2)$ 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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1802-m2017-0198},
url = {https://global-sci.com/article/84416/unconditional-superconvergence-analysis-of-an-h1-galerkin-mixed-finite-element-method-for-two-dimensional-ginzburg-landau-equation}
}