Physics-based stabilized finite element approximations of the Poisson--Nernst--Planck equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929643130454016 |
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| author | Bonilla, Jesús Gutiérrez-Santacreu, Juan Vicente |
| author_facet | Bonilla, Jesús Gutiérrez-Santacreu, Juan Vicente |
| contents | We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01358 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Physics-based stabilized finite element approximations of the Poisson--Nernst--Planck equations Bonilla, Jesús Gutiérrez-Santacreu, Juan Vicente Numerical Analysis 65M60, 35K61, 65Z05 We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through numerical experiments. |
| title | Physics-based stabilized finite element approximations of the Poisson--Nernst--Planck equations |
| topic | Numerical Analysis 65M60, 35K61, 65Z05 |
| url | https://arxiv.org/abs/2411.01358 |