Convergence of linear and nonlinear Neumann�Neumann method for the Cahn�Hilliard equation

Abstract

In this paper, we propose and analyze a non-overlapping substructuring type algorithm for the Cahn�Hilliard equation. Being a nonlinear equation, it is of great importance to develop a robust numerical method for investigating the solution behaviour of the CH equation. We present the formulation of the Neumann�Neumann method applied to the CH equation and study its convergence behaviour in one and two spatial dimension for two subdomains and also extend the method for logarithmic nonlinearity. We also present the nonlinear NN method for the CH equation. We illustrate the theoretical results by providing numerical examples. � 2023, The JJIAM Publishing Committee and Springer Nature Japan KK, part of Springer Nature.