Related papers: An energy stable fourth order finite difference sc…
We propose a novel second order in time numerical scheme for Cahn-Hilliard-Navier- Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection…
The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…
In this paper, we study a novel second-order energy stable Backward Differentiation Formula (BDF) finite difference scheme for the epitaxial thin film equation with slope selection (SS). One major challenge for the higher oder in time…
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…
In this paper we propose and analyze an energy stable numerical scheme for the square phase field crystal (SPFC) equation, a gradient flow modeling crystal dynamics at the atomic scale in space but on diffusive scales in time. In…
In this paper, a non-uniform time-stepping convex-splitting numerical algorithm for solving the widely used time-fractional Cahn-Hilliard equation is introduced. The proposed numerical scheme employs the $L1^+$ formula for discretizing the…
Efficient and unconditionally stable high order time marching schemes are very important but not easy to construct for nonlinear phase dynamics. In this paper, we propose and analysis an efficient stabilized linear Crank-Nicolson scheme for…
In this paper, we propose a novel recovery based finite element method for the Cahn-Hilliard equation. One distinguishing feature of the method is that we discretize the fourth-order differential operator in a standard $C^0$ linear finite…
We propose and analyze a first-order finite difference scheme for the functionalized Cahn-Hilliard (FCH) equation with a logarithmic Flory-Huggins potential. The semi-implicit numerical scheme is designed based on a suitable convex-concave…
Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit…
In this paper we provide a detailed convergence analysis for fully discrete second order (in both time and space) numerical schemes for nonlocal Allen-Cahn (nAC) and nonlocal Cahn-Hilliard (nCH) equations. The unconditional unique…
A finite difference numerical scheme is proposed and analyzed for the Cahn-Hilliard-Stokes system with Flory-Huggins energy functional. A convex splitting is applied to the chemical potential, which in turns leads to the implicit treatment…
This work proposes and analyzes a fully discrete numerical scheme for solving the Landau-Lifshitz-Gilbert (LLG) equation, which achieves fourth-order spatial accuracy and third-order temporal accuracy.Spatially, fourth-order accuracy is…
We present and analyze finite difference numerical schemes for the Allen Cahn/Cahn-Hilliard equation with a logarithmic Flory Huggins energy potential. Both the first order and second order accurate temporal algorithms are considered. In…
We present a numerical scheme for solving a sixth-order Cahn-Hilliard type equation that captures the dynamics of phase transitions in a ternary mixture consisting of two immiscible fluids and a surface active molecule that is amphiphilic.…
We present several first-order and second-order numerical schemes for the Cahn-Hilliard equation with discrete unconditional energy stability. These schemes stem from the generalized Positive Auxiliary Variable (gPAV) idea, and require only…
In this paper, we consider the numerical approximations for the commonly used binary fluid-surfactant phase field model that consists two nonlinearly coupled Cahn-Hilliard equations. The main challenge in solving the system numerically is…
We present an optimal rate convergence analysis for a second order accurate in time, fully discrete finite difference scheme for the Cahn-Hilliard-Navier-Stokes (CHNS) system, combined with logarithmic Flory-Huggins energy potential. The…
The main contribution of this work is to construct and analyze stable and high order schemes to efficiently solve the two-dimensional time Caputo-Fabrizio fractional diffusion equation. Based on a third-order finite difference method in…
We consider numerical approximations and error analysis for the Cahn-Hilliard equation with reaction rate dependent dynamic boundary conditions (P. Knopf et. al., arXiv, 2020). Based on the stabilized linearly implicit approach, a…