相关论文: Structure-preserving weighted BDF2 methods for Ani…

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…

In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system…

An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal model. The suggested method is proved to preserve a modified energy dissipation law at the discrete levels if the time-step ratios…

We provide a new theoretical framework for the variable-step deferred correction (DC) methods based on the well-known BDF2 formula. By using the discrete orthogonal convolution kernels, some high-order BDF2-DC methods are proven to be…

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…

An adaptive implicit-explicit (IMEX) BDF2 scheme is investigated on generalized SAV approach for the Cahn-Hilliard equation by combining with Fourier spectral method in space. It is proved that the modified energy dissipation law is…

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…

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…

The scalar auxiliary variable (SAV) approach of Shen et al. (2018), which presents a novel way to discretize a large class of gradient flows, has been extended and improved by many authors for general dissipative systems. In this work we…

Based on the equivalence of A-stability and G-stability, the energy technique of the six-step BDF method for the heat equation has been discussed in [Akrivis, Chen, Yu, Zhou, Math. Comp., Revised]. Unfortunately, this theory is hard to…

We investigate the stability of two families of three-level two-step schemes that extend the classical second order BDF (BDF2) and second order Adams-Moulton (AM2) schemes. For a free parameter restricted to an appropriate range that covers…

An energy stable conservative method is developed for the Cahn--Hilliard (CH) equation with the degenerate mobility. The CH equation is discretized in space with the mass conserving symmetric interior penalty discontinuous Galerkin (SIPG)…

We propose and analyze a structure-preserving space-time variational discretization method for the Cahn-Hilliard-Navier-Stokes system. Uniqueness and stability for the discrete problem is established in the presence of concentration…

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 and analyze a first-order and a second-order time-stepping schemes for the anisotropic phase-field dendritic crystal growth model. The proposed schemes are based on an auxiliary variable approach for the Allen-Cahn…

In this paper, we consider the numerical solution of a binary fluid-surfactant phase field model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg-Landau double well potential, and a logarithmic Flory-Huggins…

We introduce a new $\mathbf F$-modulated energy stability framework for general linear multistep methods. We showcase the theory for the two dimensional molecular beam epitaxy model with no slope selection which is a prototypical gradient…

In this paper, we propose and analyze an efficient numerical method for the anisotropic phase field dendritic crystal growth model, which is challenging because we are facing the nonlinear coupling and anisotropic coefficient in the model.…

We present a set of linear, second order, unconditionally energy stable schemes for the Allen-Cahn equation with nonlocal constraints that preserves the total volume of each phase in a binary material system. The energy quadratization…

We analyze the one-step method TR-BDF2 from the point of view of monotonicity, strong stability and positivity. All these properties are strongly related and reviewed in the common framework of absolute monotonicity. The radius of absolute…