An Implicit Midpoint Spectral Approximation of Nonlocal Cahn--Hilliard Equations

An Implicit Midpoint Spectral Approximation of Nonlocal Cahn-Hilliard Equations

The paper is concerned with the convergence analysis of a numerical method for nonlocal Cahn– Hilliard equations. The temporal discretization is based on the implicit midpoint rule and a Fourier spectral discretization is used with respect to the spatial variables. The sequence of numerical approximations in shown to be bounded in various norms, uniformly with respect to the discretization para...

Stabilized Semi-implicit Spectral Deferred Correction Methods for Allen-cahn and Cahn-hilliard Equations

Stabilized semi-implicit spectral defect correction (SSISDC) methods are constructed for the time discretization of Allen-Cahn and Cahn-Hilliard equations. These methods are unconditionally stable, lead to simple linear system to solve at each iteration and can achieve high-order time accuracy with a few iterations in each time step. Ample numerical results are presented to demonstrate the effe...

2 Finite Element Approximation of an Allen - Cahn / Cahn - Hilliard

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short tim...

Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations

Article history: Received 10 May 2013 Received in revised form 18 July 2014 Accepted 2 August 2014 Available online 8 August 2014