A fully discrete positivity-preserving and energy-dissipative finite difference scheme for Poisson–Nernst–Planck equations

2020 ◽  
Vol 145 (1) ◽  
pp. 77-115 ◽  
Author(s):  
Jingwei Hu ◽  
Xiaodong Huang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Positivity Preserving ◽  
Fully Discrete

scholarly journals INVESTIGATION OF A COST‐EFFECTIVE FINITE DIFFERENCE SCHEME FOR THE TRANSPORT EQUATION

2003 ◽  
Vol 8 (3) ◽  
pp. 247-258
Author(s):  
D. G. Slugin ◽  
A. V. Popov
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Transport Equation ◽  
Finite Difference Scheme ◽  
Three Dimensional ◽  
Cost Effective ◽  
Differential Approximation ◽  
Fully Discrete ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference

The transport equation for three‐dimensional flow of a viscous gas is considered. An implicit finite difference scheme is constructed for approximating the transport equation. The error estimation is proved. The main part of the analysis is done for the first differential approximation of the proposed finite difference scheme, but the results are also valid in the fully discrete case.

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