Supplementary variable method for thermodynamically consistent partial differential equations

Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models

(2020) Yuezheng Gong et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A new Lagrange multiplier approach for gradient flows

(2020) Qing Cheng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Arbitrarily high-order linear energy stable schemes for gradient flow models

(2020) Yuezheng Gong et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Efficient and linear schemes for anisotropic Cahn–Hilliard model using the Stabilized-Invariant Energy Quadratization (S-IEQ) approach

(2019) Zhen Xu et al.   COMPUTER PHYSICS COMMUNICATIONS

Energy-stable Runge–Kutta schemes for gradient flow models using the energy quadratization approach

(2019) Yuezheng Gong et al.   APPLIED MATHEMATICS LETTERS

Arbitrarily high-order unconditionally energy stable SAV schemes for gradient flow models

(2019) Yuezheng Gong et al.   COMPUTER PHYSICS COMMUNICATIONS

A variant of scalar auxiliary variable approaches for gradient flows

(2019) Dianming Hou et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

Regularized linear schemes for the molecular beam epitaxy model with slope selection

(2018) Lizhen Chen et al.   APPLIED NUMERICAL MATHEMATICS

The scalar auxiliary variable (SAV) approach for gradient flows

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

On the stability and accuracy of partially and fully implicit schemes for phase field modeling

(2018) Jinchao Xu et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Unconditionally stable methods for gradient flow using Convex Splitting Runge–Kutta scheme

(2017) Jaemin Shin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

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

Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations

(2016) Dong Li et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models

(2013) Xinlong Feng et al.   East Asian Journal on Applied Mathematics

An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation

(2012) Zhengru Zhang et al.   Communications in Computational Physics

Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method

(2012) E. Celledoni et al.   JOURNAL OF COMPUTATIONAL PHYSICS

On linear schemes for a Cahn–Hilliard diffuse interface model

(2012) F. Guillén-González et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy

(2012) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation

(2011) C. Wang et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A General Framework for Deriving Integral Preserving Numerical Methods for PDEs

(2011) Morten Dahlby et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Projection methods preserving Lyapunov functions

(2010) M. Calvo et al.   BIT NUMERICAL MATHEMATICS

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

Finite element approximation of nematic liquid crystal flows using a saddle-point structure

(2010) Santiago Badia et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A new class of energy-preserving numerical integration methods

(2008) G R W Quispel et al.   Journal of Physics A-Mathematical and Theoretical