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

A new Lagrange multiplier approach for gradient flows

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

The scalar auxiliary variable (SAV) approach for gradient flows

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

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

Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection

(2017) Lili Ju et al.   MATHEMATICS OF COMPUTATION

On the maximum principle preserving schemes for the generalized Allen–Cahn equation

(2016) Jie Shen et al.   Communications in Mathematical Sciences

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

(2016) Tao Tang et al.   JOURNAL OF COMPUTATIONAL 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

Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations

(2016) Qiang Du et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Long Time Numerical Simulations for Phase-Field Problems Using $p$-Adaptive Spectral Deferred Correction Methods

(2015) Xinlong Feng et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation

(2014) Zhen Guan et al.   NUMERISCHE MATHEMATIK

Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium

(2013) Hector Gomez et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Phase-Field Models for Multi-Component Fluid Flows

(2012) Junseok Kim   Communications in Computational Physics

Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models

(2011) Hector Gomez et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights

(2011) Leonardo Golubović et al.   East Asian Journal on Applied Mathematics

Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

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