Convergence of the Neumann-Neumann Method for the Cahn-Hilliard Equation

TL;DR

This paper analyzes the convergence of the Neumann-Neumann method applied to the nonlinear Cahn-Hilliard equation in one and two dimensions, providing theoretical insights and numerical validation.

Contribution

It introduces and investigates the convergence of a substructuring Neumann-Neumann method specifically for the nonlinear Cahn-Hilliard equation.

Findings

Convergence behavior established for 1D and 2D cases.

Numerical examples confirm theoretical predictions.

Abstract

In this paper, we analyze a substructuring type algorithm for the Cahn-Hilliard (CH) equation. Being a nonlinear equation, it is of great importance to develop efficient numerical schemes for investigating the solution behaviour of the CH equation. We present the formulation of Neumann-Neumann (NN) method applied to the CH equation and investigate the convergence behaviour of the same in one and two spatial dimension for two subdomains. We illustrate the theoretical results by providing numerical example.