An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations
نویسندگان
چکیده
منابع مشابه
An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations
Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources, which describe the electrodiffusion of ions in a solvated biomolecular system. In this paper, some error bounds for a piecewise finite element approximation to this problem are derived. S...
متن کاملError analysis of finite element method for Poisson-Nernst-Planck equations
In this paper we study the a priori error estimates of finite element method for the system of time-dependent Poisson–Nernst–Planck equations, and for the first time, we obtain its optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm,with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semia...
متن کاملSingular perturbation solutions of steady-state Poisson-Nernst-Planck systems.
We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively stud...
متن کاملSingular perturbation analysis of the steady-state Poisson-Nernst-Planck system: Applications to ion channels.
Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst-Planck) equations called PN...
متن کاملPoisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions
In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics and Mechanics
سال: 2013
ISSN: 2070-0733,2075-1354
DOI: 10.4208/aamm.11-m11184