A stabilized finite element method for the Poisson-Nernst-Planck equations in three-dimensional ion channel simulations

DOI10.1016/j.aml.2020.106652zbMath1448.78051OpenAlexW3045711801MaRDI QIDQ2006347

Benzhuo Lu, Qin Wang, Hongliang Li, Linbo Zhang

Publication date: 8 October 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2020.106652

zbMATH Keywords

stabilized finite element methodPoisson-Nernst-PlanckSUPGinterior penalty

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Electrochemistry (78A57)

Related Items (6)

A new block preconditioner and improved finite element solver of Poisson-Nernst-Planck equation ⋮ A class of finite element methods with averaging techniques for solving the three-dimensional drift-diffusion model in semiconductor device simulations ⋮ A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation ⋮ Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations ⋮ Error estimates for the finite element method of the Navier-Stokes-Poisson-Nernst-Planck equations ⋮ A positivity-preserving and free energy dissipative hybrid scheme for the Poisson-Nernst-Planck equations on polygonal and polyhedral meshes

Cites Work

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• Stabilized finite element methods to simulate the conductances of ion channels
• Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes. I: Finite element solutions
• Efficient and Qualified Mesh Generation for Gaussian Molecular Surface Using Adaptive Partition and Piecewise Polynomial Approximation
• A Finite Volume Scheme for Nernst-Planck-Poisson Systems with Ion Size and Solvation Effects
• Theory of the Flow of Electrons and Holes in Germanium and Other Semiconductors

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