A High-Order and Unconditionally Energy Stable Scheme for the Conservative Allen–Cahn Equation with a Nonlocal Lagrange Multiplier

An Energy Stable Finite Element Scheme for the Three-Component Cahn–Hilliard-Type Model for Macromolecular Microsphere Composite Hydrogels

(2021) Maoqin Yuan et al.   JOURNAL OF SCIENTIFIC COMPUTING

Arbitrarily high order structure-preserving algorithms for the Allen-Cahn model with a nonlocal constraint

(2021) Qi Hong et al.   APPLIED NUMERICAL MATHEMATICS

The numerical solutions for the energy-dissipative and mass-conservative Allen–Cahn equation

(2020) Dongsun Lee   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Energy Stable Numerical Schemes for Ternary Cahn-Hilliard System

(2020) Wenbin Chen et al.   JOURNAL OF SCIENTIFIC COMPUTING

Second Order Linear Energy Stable Schemes for Allen-Cahn Equations with Nonlocal Constraints

(2019) Xiaobo Jing et al.   JOURNAL OF SCIENTIFIC COMPUTING

A stable and structure-preserving scheme for a non-local Allen–Cahn equation

(2018) Makoto Okumura   JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS

Error Estimates of Energy Stable Numerical Schemes for Allen–Cahn Equations with Nonlocal Constraints

(2018) Shouwen Sun et al.   JOURNAL OF SCIENTIFIC COMPUTING

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

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

First and second order numerical methods based on a new convex splitting for phase-field crystal equation

(2016) Jaemin Shin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Investigations on several numerical methods for the non-local Allen–Cahn equation

(2015) Shuying Zhai et al.   INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER

A conservative Allen–Cahn equation with a space–time dependent Lagrange multiplier

(2014) Junseok Kim et al.   INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE

Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation

(2013) Arvind Baskaran et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A modified phase field approximation for mean curvature flow with conservation of the volume

(2011) M. Brassel et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities

(2010) Jie Shen et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

An efficient moving mesh spectral method for the phase-field model of two-phase flows

(2009) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation

(2009) Z. Hu et al.   JOURNAL OF COMPUTATIONAL PHYSICS