Convergence Analysis for the Invariant Energy Quadratization (IEQ) Schemes for Solving the Cahn–Hilliard and Allen–Cahn Equations with General Nonlinear Potential

Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn-Hilliard Model

(2019) Chuanjun Chen et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Efficient linear, stabilized, second-order time marching schemes for an anisotropic phase field dendritic crystal growth model

(2019) Xiaofeng Yang   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Efficient numerical scheme for a dendritic solidification phase field model with melt convection

(2019) Chuanjun Chen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Energy Stable Linear Schemes for Mass-Conserved Gradient Flows with Peng-Robinson Equation of State

(2019) Qiujin Peng   East Asian Journal on Applied Mathematics

A novel decoupled and stable scheme for an anisotropic phase-field dendritic crystal growth model

(2019) Jun Zhang et al.   APPLIED MATHEMATICS LETTERS

Finite element simulation and efficient algorithm for fractional Cahn–Hilliard equation

(2019) Feng Wang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Efficient modified techniques of invariant energy quadratization approach for gradient flows

(2019) Zhengguang Liu et al.   APPLIED MATHEMATICS LETTERS

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

(2018) Lizhen Chen et al.   APPLIED NUMERICAL MATHEMATICS

Optimal L∞(L2) error analysis of a direct discontinuous Galerkin method for a time-fractional reaction-diffusion problem

(2018) Chaobao Huang et al.   BIT NUMERICAL MATHEMATICS

Mixed volume element combined with characteristic mixed finite volume element method for oil–water two phase displacement problem

(2018) Yirang Yuan et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Linear, second order and unconditionally energy stable schemes for the viscous Cahn–Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method

(2018) Xiaofeng Yang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Stabilized linear semi-implicit schemes for the nonlocal Cahn–Hilliard equation

(2018) Qiang Du et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Decoupled, Linear, and Energy Stable Finite Element Method for the Cahn--Hilliard--Navier--Stokes--Darcy Phase Field Model

(2018) Yali Gao et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Efficient Second Order Unconditionally Stable Schemes for a Phase Field Moving Contact Line Model Using an Invariant Energy Quadratization Approach

(2018) Xiaofeng Yang et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Unconditionally Energy Stable Linear Schemes for the Diffuse Interface Model with Peng–Robinson Equation of State

(2017) Hongwei Li et al.   JOURNAL OF SCIENTIFIC COMPUTING

A mixed-type Galerkin variational formulation and fast algorithms for variable-coefficient fractional diffusion equations

(2017) Yongshan Li et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method

(2017) Xiaofeng Yang et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Second Order, Linear, and Unconditionally Energy Stable Schemes for a Hydrodynamic Model of Smectic-A Liquid Crystals

(2017) Rui Chen et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Numerical approximations to a new phase field model for two phase flows of complex fluids

(2016) Jia Zhao et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Discontinuous Galerkin immersed finite element methods for parabolic interface problems

(2016) Qing Yang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends

(2016) Xiaofeng Yang   JOURNAL OF COMPUTATIONAL PHYSICS

Mixed-Type Galerkin Variational Principle and Numerical Simulation for a Generalized Nonlocal Elastic Model

(2016) Lueling Jia et al.   JOURNAL OF SCIENTIFIC COMPUTING

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

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

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

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

Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs

(2015) Wei Gong et al.   JOURNAL OF SCIENTIFIC COMPUTING

Local discontinuous Galerkin approximation of non-Fickian diffusion model in viscoelastic polymers

(2014) Zhaojie Zhou et al.   APPLICABLE ANALYSIS

Efficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn-Hilliard Systems

(2012) Feng Chen et al.   Communications in 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

Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

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

Phase-field modeling of the dynamics of multicomponent vesicles: Spinodal decomposition, coarsening, budding, and fission

(2009) John S. Lowengrub et al.   PHYSICAL REVIEW E