A Structure-Preserving, Upwind-SAV Scheme for the Degenerate Cahn–Hilliard Equation with Applications to Simulating Surface Diffusion

Linear multi-step methods and their numerical stability for solving gradient flow equations

(2023) Qiong-Ao Huang et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

Benchmark Computations of the Phase Field Crystal and Functionalized Cahn-Hilliard Equations via Fully Implicit, Nesterov Accelerated Schemes

(2023) Jea-Hyun Park et al.   Communications in Computational Physics

Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation

(2023) Rafael Bailo et al.   Communications in Computational Physics

Arbitrarily High-Order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen–Cahn Equations

(2022) Jiang Yang et al.   JOURNAL OF SCIENTIFIC COMPUTING

A new Lagrange multiplier approach for constructing structure preserving schemes, I. Positivity preserving

(2022) Qing Cheng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Improving the accuracy and consistency of the scalar auxiliary variable (SAV) method with relaxation

(2022) Maosheng Jiang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Energy-decreasing exponential time differencing Runge–Kutta methods for phase-field models

(2022) Zhaohui Fu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Approximation of surface diffusion flow: A second-order variational Cahn–Hilliard model with degenerate mobilities

(2022) Elie Bretin et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving

(2022) Qing Cheng et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Bound/positivity preserving and unconditionally stable schemes for a class of fourth order nonlinear equations

(2022) Fukeng Huang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Stabilized Exponential-SAV Schemes Preserving Energy Dissipation Law and Maximum Bound Principle for The Allen–Cahn Type Equations

(2022) Lili Ju et al.   JOURNAL OF SCIENTIFIC COMPUTING

An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model

(2022) Daniel Acosta-Soba et al.   NUMERICAL ALGORITHMS

Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows

(2022) Lili Ju et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Unconditionally Maximum Bound Principle Preserving Linear Schemes for the Conservative Allen–Cahn Equation with Nonlocal Constraint

(2021) Jingwei Li et al.   JOURNAL OF SCIENTIFIC COMPUTING

Supplementary variable method for thermodynamically consistent partial differential equations

(2021) Yuezheng Gong et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

On a non-isothermal Cahn-Hilliard model for tumor growth

(2021) Erica Ipocoana   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

A new Lagrange multiplier approach for gradient flows

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

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

(2020) Qi Hong et al.   APPLIED MATHEMATICS LETTERS

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

An unconditionally energy stable scheme for simulating wrinkling phenomena of elastic thin films on a compliant substrate

(2019) Qiong-Ao Huang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An Efficient and Unconditionally Energy Stable Scheme for Simulating Solid-State Dewetting of Thin Films with Isotropic Surface Energy†

(2019) Qiong-Ao Huang   Communications in Computational Physics

The scalar auxiliary variable (SAV) approach for gradient flows

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

A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis

(2018) Harald Garcke et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Sharp-interface approach for simulating solid-state dewetting in two dimensions: A Cahn–Hoffman ξ-vector formulation

(2018) Wei Jiang et al.   PHYSICA D-NONLINEAR PHENOMENA

Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle

(2016) Tao Tang et al.   JOURNAL OF COMPUTATIONAL MATHEMATICS

Sharp-Interface Limits of the Cahn--Hilliard Equation with Degenerate Mobility

(2016) Alpha Albert Lee et al.   SIAM JOURNAL ON APPLIED MATHEMATICS

Weak Solutions for the Cahn–Hilliard Equation with Degenerate Mobility

(2015) Shibin Dai et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and Lubrication-type equations

(2013) Changna Lu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Phase field approach for simulating solid-state dewetting problems

(2012) Wei Jiang et al.   ACTA MATERIALIA

A Finite Volume Scheme for Nonlinear Degenerate Parabolic Equations

(2012) Marianne Bessemoulin-Chatard et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images

(2009) Martin Burger et al.   SIAM Journal on Imaging Sciences