Stability and error analysis of pressure-correction scheme for the Navier-Stokes-Planck-Nernst-Poisson equations
<|reference_start|>Stability and error analysis of pressure-correction scheme for the Navier-Stokes-Planck-Nernst-Poisson equations: In this paper, we propose and analyze first-order time-stepping pressure-correction projection scheme for the Navier-Stokes-Planck-Nernst-Poisson equations. By introducing a governing equation for the auxiliary variable through the ionic concentration equations, we reconstruct the original equations into an equivalent system and develop a first-order decoupled and linearized scheme. This scheme preserves non-negativity and mass conservation of the concentration components and is unconditionally energy stable. We derive the rigorous error estimates in the two dimensional case for the ionic concentrations, electric potential, velocity and pressure in the $L^2$- and $H^1$-norms. Numerical examples are presented to validate the proposed scheme.<|reference_end|>
@article{he2024stability,
    title={Stability and error analysis of pressure-correction scheme for the
  Navier-Stokes-Planck-Nernst-Poisson equations},
    author={Yuyu He and Hongtao Chen},
    journal={arXiv preprint arXiv:2408.06085},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.06085},
    primaryClass={math.NA cs.NA}
}