96 citations · 484 across the 29 of their papers we have counts for
11 papers · 1 filter
A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance
Chun Liu, Cheng Wang, Yiwei Wang
In this paper, we propose and analyze a positivity-preserving, energy stable numerical scheme for certain type reaction-diffusion systems involving the Law of Mass Action with the…
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…
On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems
Patrik Knopf, Chun Liu
In this paper, we study second-order and fourth-order elliptic problems which include not only a Poisson equation in the bulk but also an inhomogeneous Laplace--Beltrami equation o…
The Brinkman-Fourier System with Ideal Gas Equilibrium
Chun Liu, Jan-Eric Sulzbach
In this work, we will introduce a general framework to derive the thermodynamics of a fluid mechanical system, which guarantees the consistence between the energetic variational ap…
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…
Particle-based Energetic Variational Inference
Yiwei Wang, Jiuhai Chen, Chun Liu +1
We introduce a new variational inference (VI) framework, called energetic variational inference (EVI). It minimizes the VI objective function based on a prescribed energy-dissipati…
Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions
Patrik Knopf, Kei Fong Lam, Chun Liu +1
The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interacti…
A Variational Lagrangian Scheme for a Phase Field Model: A Discrete Energetic Variational Approach
Chun Liu, Yiwei Wang
In this paper, we propose a variational Lagrangian scheme for a modified phase-field model, which can compute the equilibrium states for the original Allen-Cahn type model. Our dis…
Global Existence of the Non-isothermal Poisson-Nernst-Planck-Fourier System
Chia-Yu Hsieh, Tai-Chia Lin, Chun Liu +1
In this paper, we consider a non-isothermal electrokinetic model, which is derived from the Energetic Variational Approach. The charge transport is described through the Poisson-Ne…
Field Theory of Reaction-Diffusion: Mass Action with an Energetic Variational Approach
Yiwei Wang, Chun Liu, Pei Liu +1
We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation la…