Discontinuous Galerkin IMEX Pressure Correction Scheme for the Poisson-Nernst-Planck-Navier-Stokes Equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915970534080512 |
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| author | Bir, Bikram Pani, Amiya K. |
| author_facet | Bir, Bikram Pani, Amiya K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27512 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discontinuous Galerkin IMEX Pressure Correction Scheme for the Poisson-Nernst-Planck-Navier-Stokes Equations Bir, Bikram Pani, Amiya K. Numerical Analysis 65M60 (Primary), 65M15, 35Q30 (Secondary) 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. |
| title | Discontinuous Galerkin IMEX Pressure Correction Scheme for the Poisson-Nernst-Planck-Navier-Stokes Equations |
| topic | Numerical Analysis 65M60 (Primary), 65M15, 35Q30 (Secondary) |
| url | https://arxiv.org/abs/2604.27512 |