相关论文: Positivity-preserving, energy stable numerical sch…

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…

In this paper, we consider the numerical approximations for the fourth order Cahn-Hilliard equation with concentration dependent mobility, and the logarithmic Flory-Huggins potential. One challenge in solving such a diffusive system…

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…

In this paper we propose and analyze a finite difference numerical scheme for the Flory-Huggins-Cahn-Hilliard equation with dynamical boundary condition. The singular logarithmic potential is included in the Flory-Huggins energy expansion.…

In this paper, two finite difference numerical schemes are proposed and analyzed for the droplet liquid film model, with a singular Leonard-Jones energy potential involved. Both first and second order accurate temporal algorithms are…

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…

A high-order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the $Q_k$ finite element with mass lumping on rectangular grids, the second-order…

We present a second-order-in-time finite difference scheme for the Cahn-Hilliard-Hele-Shaw equations. This numerical method is uniquely solvable and unconditionally energy stable. At each time step, this scheme leads to a system of…

The Allen--Cahn equation is one of fundamental equations of phase-field models, while the logarithmic Flory--Huggins potential is one of the most useful energy potentials in various phase-field models. In this paper, we consider numerical…

We study the numerical algorithm and error analysis for the Cahn-Hilliard equation with dynamic boundary conditions. A second-order in time, linear and energy stable scheme is proposed, which is an extension of the first-order stabilized…

In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that our two-step scheme is unconditionally energy stable and…

We present and analyze an unconditionally energy stable and convergent finite difference scheme for the Functionalized Cahn-Hilliard equation. One key difficulty associated with the energy stability is based on the fact that one nonlinear…

In this paper, we construct and analyze a uniquely solvable, positivity preserving and unconditionally energy stable finite-difference scheme for the periodic three-component Macromolecular Microsphere Composite (MMC) hydrogels system, a…

We present and analyze a new second-order finite difference scheme for the Macromolecular Microsphere Composite hydrogel, Time-Dependent Ginzburg-Landau (MMC-TDGL) equation, a Cahn-Hilliard equation with Flory-Huggins-deGennes energy…

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 with Flory-Huggins potential serves as a fundamental phase field model for describing phase separation phenomena. Due to the presence of logarithmic singularities at $u=\pm 1$, the solution $u$ is constrained…

A second order accurate numerical scheme is proposed and analyzed for the periodic three-component Macromolecular Microsphere Composite(MMC) hydrogels system, a ternary Cahn-Hilliard system with a Flory-Huggins-deGennes free energy…

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 approximation in space. In particular, the truncation error for…

We consider the two-dimensional Cahn-Hilliard equation with logarithmic potentials and periodic boundary conditions. We employ the standard semi-implicit numerical scheme which treats the linear fourth-order dissipation term implicitly and…

We present a finite-volume based numerical scheme for a nonlocal Cahn-Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn-Hilliard equations. The equation of interest is a…