Finite difference schemes for Cahn-Hilliard equation

June 2, 2007

Title: Conservative nonlinear difference scheme for the Cahn-Hilliard equation (Parts I and II)

Authors: S M Choo and S K Chung (Part I); S M Choo, S K Chung and K I Kim(Part II)

Source: Part I — Computers and Mathematics with applications, Vol. 36, Issue 7, October 1998, pp. 31-39; Part II — Computers and Mathematics with applications, Vol . 39, Issues 1-2, January 2000, pp. 229-243.

Abstract:

Part I:

Numerical solutions for the Cahn-Hilliard equation is considered using the Crank-Nicolson type finite difference method. Existence of the solution for the difference scheme has been shown by Brouwer fixed-point theorem. Stability, convergence and error analysis of the scheme are shown. We also show that the scheme preserves the discrete mass, even though the linearized scheme in [1] is conditionally stable and does not preserve the mass.

Part II:

A nonlinear conservative difference scheme is considered for the two-dimensional Cahn-Hilliard equation. Existence of the solution for the finite difference scheme has been shown and the corresponding stability, convergence, and error estimates are discussed. We also show that the scheme preserves the discrete total mass computationally as well as analytically.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: