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A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system
In this paper we propose and analyze a finite difference numerical scheme for the Poisson-
Nernst-Planck equation (PNP) system. To understand the energy structure of the PNP …
Nernst-Planck equation (PNP) system. To understand the energy structure of the PNP …
Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions
This paper presents two kinds of strategies to construct structure-preserving algorithms with
homogeneous Neumann boundary conditions for the sine-Gordon equation, while most …
homogeneous Neumann boundary conditions for the sine-Gordon equation, while most …
Unconditionally positivity preserving and energy dissipative schemes for Poisson–Nernst–Planck equations
We develop a set of numerical schemes for the Poisson–Nernst–Planck equations. We
prove that our schemes are mass conservative, uniquely solvable and keep positivity …
prove that our schemes are mass conservative, uniquely solvable and keep positivity …
Efficient, positive, and energy stable schemes for multi-D Poisson–Nernst–Planck systems
In this paper, we design, analyze, and numerically validate positive and energy-dissipating
schemes for solving the time-dependent multi-dimensional system of Poisson–Nernst …
schemes for solving the time-dependent multi-dimensional system of Poisson–Nernst …
Positivity Preserving and Mass Conservative Projection Method for the Poisson–Nernst–Planck Equation
We propose and analyze a novel approach to construct structure preserving approximations
for the Poisson–Nernst–Planck equations, focusing on the positivity preserving and mass …
for the Poisson–Nernst–Planck equations, focusing on the positivity preserving and mass …
Linearized conservative finite element methods for the Nernst–Planck–Poisson equations
The aim of this paper is to present and study new linearized conservative schemes with finite
element approximations for the Nernst–Planck–Poisson equations. For the linearized …
element approximations for the Nernst–Planck–Poisson equations. For the linearized …
A positivity preserving and free energy dissipative difference scheme for the Poisson–Nernst–Planck system
In this paper, based on the reformulation of the Nernst–Planck equations, we construct an
unconditionally stable semi-implicit linearized difference scheme for the time dependent …
unconditionally stable semi-implicit linearized difference scheme for the time dependent …
An unconditionally energy stable linear scheme for Poisson–Nernst–Planck equations
This paper proposes a linear, unconditionally energy-stable scheme for the Poisson–Nernst–
Planck (PNP) equations. Based on a gradient-flow formulation of the PNP equations, the …
Planck (PNP) equations. Based on a gradient-flow formulation of the PNP equations, the …
Positivity-preserving third order DG schemes for Poisson–Nernst–Planck equations
In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin
(DG) schemes for solving the time-dependent system of Poisson–Nernst–Planck (PNP) …
(DG) schemes for solving the time-dependent system of Poisson–Nernst–Planck (PNP) …
A dynamic mass transport method for Poisson-Nernst-Planck equations
A dynamic mass-transport method is proposed for approximately solving the Poisson–
Nernst–Planck (PNP) equations. The semi-discrete scheme based on the JKO type …
Nernst–Planck (PNP) equations. The semi-discrete scheme based on the JKO type …