Supplementary variable method for structure-preserving approximations to partial differential equations with deduced equations

A roadmap for discretely energy-stable schemes for dissipative systems based on a generalized auxiliary variable with guaranteed positivity

(2019) Zhiguo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Second Order Fully Discrete Energy Stable Methods on Staggered Grids for Hydrodynamic Phase Field Models of Binary Viscous Fluids

(2018) Yuezheng Gong et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method

(2017) Xiaofeng Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Biological transportation networks: Modeling and simulation

(2016) Giacomo Albi et al.   Analysis and Applications

Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle

(2016) Xiaogang Yang et al.   Entropy

Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach

(2016) Jia Zhao et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

On Second Order Semi-implicit Fourier Spectral Methods for 2D Cahn–Hilliard Equations

(2016) Dong Li et al.   JOURNAL OF SCIENTIFIC COMPUTING

Notes on a PDE system for biological network formation

(2016) Jan Haskovec et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Mathematical Analysis of a PDE System for Biological Network Formation

(2015) Jan Haskovec et al.   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

Second order convex splitting schemes for periodic nonlocal Cahn–Hilliard and Allen–Cahn equations

(2014) Zhen Guan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Adaptation and Optimization of Biological Transport Networks

(2013) Dan Hu et al.   PHYSICAL REVIEW LETTERS

Unconditionally stable schemes for equations of thin film epitaxy

(2010) Steven Wise et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

(2010) Jie Shen et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Unconditionally Stable Finite Difference, Nonlinear Multigrid Simulation of the Cahn-Hilliard-Hele-Shaw System of Equations

(2010) S. M. Wise   JOURNAL OF SCIENTIFIC COMPUTING