29 citations · 51 across the 11 of their papers we have counts for
11 papers
A refined convergence estimate for a fourth order finite difference numerical scheme to the Cahn-Hilliard equation
Jing Guo, Cheng Wang, Yue Yan +1
In this article we present a refined convergence analysis for a second order accurate in time, fourth order finite difference numerical scheme for the 3-D Cahn-Hilliard equation, w…
A second order accurate numerical method for the Poisson-Nernst-Planck system in the energetic variational formulation
Chun Liu, Cheng Wang, Steven M. Wise +2
A second order accurate (in time) numerical scheme is proposed and analyzed for the Poisson-Nernst-Planck equation (PNP) system, reformulated as a non-constant mobility gr…
Homogenization Theory of Ion Transportation in Multicellular Tissue
Chun Xiao, Xingye Yue, Huaxiong Huang +1
Ion transport in biological tissues is crucial in the study of many biological and pathological problems. Some multi-cellular structures, like smooth muscles on the vessel walls, c…
A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system
Chun Liu, Cheng Wang, Steven M. Wise +2
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 model,…
Structure-Preserving Numerical Methods for Nonlinear Fokker--Planck Equations with Nonlocal Interactions by an Energetic Variational Approach
Chenghua Duan, Wenbin Chen, Chun Liu +2
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many ca…
A second order accurate numerical scheme for the porous medium equation by an energetic variational approach
Chenghua Duan, Wenbin Chen, Chun Liu +2
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the traject…
Convergence analysis of a numerical scheme for the porous medium equation by an energetic variational approach
Chenghua Duan, Chun Liu, Cheng Wang +1
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. We have studied numerical methods for PME by an energetic variational approach in [C. Duan et…
Numerical methods for Porous Medium Equation by an Energetic Variational Approach
Chenghua Duan, Chun Liu, Cheng Wang +1
We study numerical methods for porous media equation (PME). There are two important characteristics: the finite speed propagation of the free boundary and the potential waiting tim…
Numerical Complete Solution for Random Genetic Drift by Energetic Variational Approach
Chenghua Duan, Chun Liu, Cheng Wang +1
In this paper, we focus on numerical solutions for random genetic drift problem, which is governed by a degenerated convection-dominated parabolic equation. Due to the fixation phe…
Behavior of different numerical schemes for population genetic drift problems
Minxin Chen, Chun Liu, Shixin Xu +2
In this paper, we focus on numerical methods for the genetic drift problems, which is governed by a degenerated convection-dominated parabolic equation. Due to the degeneration and…
Multi-scale Modeling for Piezoelectric Composite Materials
Qian Zhang, Xingye Yue
In this paper, we focus on multi-scale modeling and simulation of piezoelectric composite materials. A multi-scale model for piezoelectric composite materials under the framework o…