Abstract
In this paper, a complete mixed finite element method is developed for a modified Poisson–Nernst–Planck/Navier–Stokes (PNP/NS) coupling system, where the original Poisson equation in PNP system is replaced by a fourth-order elliptic equation to more precisely account for electrostatic correlations in a simplified form of the Landau–Ginzburg-type continuum model. A stabilized mixed weak form is defined for each equation of the modified PNP/NS model in terms of primary variables and their corresponding vector-valued gradient variables, based on which a stable Stokes-pair mixed finite element is thus able to be utilized to discretize all solutions to the entire modified PNP/NS model in the framework of Stokes-type mixed finite element approximation. Semi- and fully discrete mixed finite element schemes are developed and are analyzed for the presented modified PNP/NS equations, and optimal convergence rates in energy norms are obtained for both schemes. Numerical experiments are carried out to validate all attained theoretical results.
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Acknowledgements
M. He is partially supported by Natural Science Foundation of Zhejiang Province, China (Nos. LY21A010011 and LQ19A010009). P. Sun was supported by a Grant from the Simons Foundation (MPS-706640, PS).
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He, M., Sun, P. Mixed Finite Element Method for Modified Poisson–Nernst–Planck/Navier–Stokes Equations. J Sci Comput 87, 80 (2021). https://doi.org/10.1007/s10915-021-01478-z
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DOI: https://doi.org/10.1007/s10915-021-01478-z
Keywords
- Modified Poisson–Nernst–Planck/Navier–Stokes (PNP/NS) coupling system
- Fourth-order elliptic equation
- A stabilized mixed finite element
- Taylor–Hood mixed element
- Optimal convergence