2025/11/26 by Xianxian Cao, Cao, Xianxian, Zhen Guan +3
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Model Reduction and Neural Networks #Electromagnetic Simulation and Numerical Methods
paper · pdf · doi:10.48550/arxiv.2511.21168
In this paper, a fully implicit Crank-Nicolson discontinuous Galerkin method is proposed for solving the Ginzburg-Landau equation. By leveraging a novel analytical technique, we rigorously establish the unique solvability of the constructed numerical scheme, as well as its unconditionally optimal error estimates under both the \(L2\)-norm and the energy norm. The core of the proof hinges on the \(L2\)-norm boundedness of the numerical solution and the refined estimation of the cubic nonlinear term. Finally, two numerical examples are presented to validate the theoretical findings.