A positivity-preserving and free energy dissipative hybrid scheme for the Poisson-Nernst-Planck equations on polygonal and polyhedral meshes

Su, Shuai; Tang, Hao

doi:10.1016/j.camwa.2021.12.019

Cited by 6 publications

(1 citation statement)

References 55 publications

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“…One can cite the discrete duality finite volume (DDFV) scheme of Chainais-Hillairet [15], which can handle general polygonal meshes with d = 2 in the framework of Boltzmann statistics. More recently, Su and Tang designed and analysed a scheme for Poisson-Nernst-Planck systems on general meshes in [38]. This scheme is based on two discretisation methods: a virtual element method for the Poisson equation alongside with a positive nonlinear finite volume method [7,8] for the convection-diffusion ones.…”

Section: Introductionmentioning

confidence: 99%

A structure preserving hybrid finite volume scheme for semi-conductor models with magnetic field on general meshes

Moatti¹

2022

Preprint

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We are interested in the discretisation of a drift-diffusion system in the framework of hybrid finite volume (HFV) methods on general polygonal/polyhedral meshes. The system under study is composed of two anisotropic and nonlinear convection-diffusion equations coupled with a Poisson equation and describes in particular semi-conductor devices immersed in a magnetic field. We introduce a new scheme based on an entropy-dissipation relation and prove that the scheme admits solutions with values in admissible sets -especially, the computed densities remain positive. Moreover, we show that the discrete solutions to the scheme converge exponentially fast in time towards the associated discrete thermal equilibrium. Several numerical tests confirm our theoretical results.

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Section: Introductionmentioning

confidence: 99%

A structure preserving hybrid finite volume scheme for semi-conductor models with magnetic field on general meshes

Moatti¹

2022

Preprint

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Error estimates for the finite element method of the Navier-Stokes-Poisson-Nernst-Planck equations

Li,

2024

Applied Numerical Mathematics

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A weak Galerkin finite element method for 1D semiconductor device simulation models

Li,

Liu,

Gao

et al. 2024

Journal of Computational and Applied Mathematics

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A positivity-preserving and free energy dissipative hybrid scheme for the Poisson-Nernst-Planck equations on polygonal and polyhedral meshes

Cited by 6 publications

References 55 publications

A structure preserving hybrid finite volume scheme for semi-conductor models with magnetic field on general meshes

A structure preserving hybrid finite volume scheme for semi-conductor models with magnetic field on general meshes

Error estimates for the finite element method of the Navier-Stokes-Poisson-Nernst-Planck equations

A weak Galerkin finite element method for 1D semiconductor device simulation models

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