@article{Guan2025, 
author = {Zhen Guan and Xianxian Cao},
title = {Weighted implicit-explicit discontinuous Galerkin methods for two-dimensional Ginzburg–Landau equations on general meshes},
year = {2025},
journal = {Networks and Heterogeneous Media},
volume = {20},
number = {4},
pages = {1367-1391},
keywords = {Ginzburg–Landau equations, discontinuous Galerkin method, general meshes, discontinuous Galerkin inverse inequality, optimal error estimate},
url = {https://www.sciopen.com/article/10.3934/nhm.2025059},
doi = {10.3934/nhm.2025059},
abstract = {In this paper, a second-order linearized discontinuous Galerkin method on general meshes, which treats the backward differentiation formula of order two (BDF2) and Crank–Nicolson schemes as special cases, is proposed for solving the two-dimensional Ginzburg–Landau equations with cubic nonlinearity. By utilizing the discontinuous Galerkin inverse inequality and the mathematical induction method, the unconditionally optimal error estimate in        L    2  -norm is obtained. The core of the analysis in this paper resides in the classification and discussion of the relationship between the temporal step size    τ and the spatial step size    h, specifically distinguishing between the two scenarios of        τ    2    ≤      h          k      +      1       and        τ    2    >      h          k      +      1      , where    k denotes the degree of the discrete spatial scheme. Finally, this paper presents two numerical examples involving various grids and polynomial degrees to verify the correctness of the theoretical results.}
}