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arXiv · 2604.27512

Discontinuous Galerkin IMEX Pressure Correction Scheme for the Poisson-Nernst-Planck-Navier-Stokes Equations

Bikram Bir·Amiya K. Pani
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Abstract

Based on a discontinuous Galerkin method in the spatial directions and an improved implicit-explicit pressure-correction scheme in the temporal direction, this paper discusses a fully discrete scheme for the Poisson-Nernst-Planck-Navier-Stokes equations. Optimal error estimates are derived in $L^2$ and in the energy norms for the concentrations of positive and negative ions, the electrostatic potential, the fluid velocity, and the $L^2$ norm of the fluid pressure. The discrete mass conservation properties of both ions are established. Finally, numerical simulations are performed, whose results confirm our theoretical findings.

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Bikram Bir, Amiya K. Pani. 2026-04-30. Discontinuous Galerkin IMEX Pressure Correction Scheme for the Poisson-Nernst-Planck-Navier-Stokes Equations. https://arxiv.org/abs/2604.27512

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