The phase field method for geometric moving interfaces and their numerical approximations
This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …
surface evolution and related geometric nonlinear partial differential equations (PDEs) …
Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows
J Shen, J Xu - SIAM Journal on Numerical Analysis, 2018 - SIAM
We carry out convergence and error analysis of the scalar auxiliary variable (SAV) methods
for L^2 and H^-1 gradient flows with a typical form of free energy. We first derive H^2 …
for L^2 and H^-1 gradient flows with a typical form of free energy. We first derive H^2 …
Isogeometric analysis of the Cahn–Hilliard phase-field model
The Cahn–Hilliard equation involves fourth-order spatial derivatives. Finite element
solutions are not common because primal variational formulations of fourth-order operators …
solutions are not common because primal variational formulations of fourth-order operators …
Second-order convex splitting schemes for gradient flows with Ehrlich–Schwoebel type energy: application to thin film epitaxy
We construct unconditionally stable, unconditionally uniquely solvable, and second-order
accurate (in time) schemes for gradient flows with energy of the form \int_Ω(F(∇ϕ(\bfx))+ϵ …
accurate (in time) schemes for gradient flows with energy of the form \int_Ω(F(∇ϕ(\bfx))+ϵ …
Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential
In this paper we present and analyze finite difference numerical schemes for the Cahn-
Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second …
Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second …
A novel fully-decoupled, second-order and energy stable numerical scheme of the conserved Allen–Cahn type flow-coupled binary surfactant model
X Yang - Computer Methods in Applied Mechanics and …, 2021 - Elsevier
In this paper, we establish a binary fluid surfactant model by coupling two mass-conserved
Allen–Cahn equations and the Navier–Stokes equations and consider numerical …
Allen–Cahn equations and the Navier–Stokes equations and consider numerical …
On energy dissipation theory and numerical stability for time-fractional phase-field equations
For the time-fractional phase-field models, the corresponding energy dissipation law has not
been well studied on both the continuous and the discrete levels. In this work, we address …
been well studied on both the continuous and the discrete levels. In this work, we address …
The Cahn-Hilliard model for the kinetics of phase separation
CM Elliott - Mathematical models for phase change problems, 1989 - Springer
In this paper we consider the Cahn-Hilliard mathematical continuum model of spinodal
decomposition (or phase separation) of a binary alloy. The phenomenological model is …
decomposition (or phase separation) of a binary alloy. The phenomenological model is …
[HTML][HTML] An energy stable fourth order finite difference scheme for the Cahn–Hilliard equation
In this paper we propose and analyze an energy stable numerical scheme for the Cahn–
Hilliard equation, with second order accuracy in time and the fourth order finite difference …
Hilliard equation, with second order accuracy in time and the fourth order finite difference …
Generalized SAV-exponential integrator schemes for Allen--Cahn type gradient flows
The energy dissipation law and the maximum bound principle (MBP) are two important
physical features of the well-known Allen--Cahn equation. While some commonly used first …
physical features of the well-known Allen--Cahn equation. While some commonly used first …