Related papers: Error estimates for the Cahn--Hilliard equation wi…
A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface…
A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite…
In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order…
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 provide a detailed convergence analysis for a first order stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation, which follows from consistency and stability estimates for the numerical…
We consider the numerical approximations of the Cahn-Hilliard equation with dynamic boundary conditions (C. Liu et. al., Arch. Rational Mech. Anal., 2019). We propose a first-order in time, linear and energy stable numerical scheme, which…
This work addresses the problem of solving the Cahn-Hilliard equation numerically. For that we introduce an abstract formulation for Cahn-Hilliard type equations with dynamic boundary conditions, we conduct the spatial semidiscretization…
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial…
We study two fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation on an evolving surface, given a smooth potential with polynomial growth. In particular we establish optimal order error bounds for a (fully…
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…
In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward…
In this paper, we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation. The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for…
In two recent publications [Kov{\'a}cs, Larsson, and Mesforush, SIAM J. Numer. Anal. 49(6), 2407-2429, 2011] and [Furihata, et al., SIAM J. Numer. Anal. 56(2), 708-731, 2018], strong convergence of the semi-discrete and fully discrete…
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…
This paper deals with time stepping schemes for the Cahn--Hilliard equation with three different types of dynamic boundary conditions. The proposed schemes of first and second order are mass-conservative and energy-dissipative and -- as…
We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise. The spatial (resp. temporal) discretization is performed…
The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation…
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…
Implicit-Explicit methods have been widely used for the efficient numerical simulation of phase field problems such as the Cahn-Hilliard equation or thin film type equations. Due to the lack of maximum principle and stiffness caused by the…
We study the numerical solution of a Cahn-Hilliard/Allen-Cahn system with strong coupling through state and gradient dependent non-diagonal mobility matrices. A fully discrete approximation scheme in space and time is proposed which…