Optimal $L^2$ error estimates of mass- and energy-conserved FE schemes for a nonlinear Schr\"odinger-type system
Numerical Analysis
2024-05-14 v2 Numerical Analysis
Abstract
In this paper, we present an implicit Crank-Nicolson finite element (FE) scheme for solving a nonlinear Schr\"odinger-type system, which includes Schr\"odinger-Helmholz system and Schr\"odinger-Poisson system. In our numerical scheme, we employ an implicit Crank-Nicolson method for time discretization and a conforming FE method for spatial discretization. The proposed method is proved to be well-posedness and ensures mass and energy conservation at the discrete level. Furthermore, we prove optimal error estimates for the fully discrete solutions. Finally, some numerical examples are provided to verify the convergence rate and conservation properties.
Keywords
Cite
@article{arxiv.2309.05967,
title = {Optimal $L^2$ error estimates of mass- and energy-conserved FE schemes for a nonlinear Schr\"odinger-type system},
author = {Zhuoyue Zhang and Wentao Cai},
journal= {arXiv preprint arXiv:2309.05967},
year = {2024}
}