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

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...

Full description

Saved in:
Bibliographic Details
Published in:Japan journal of industrial and applied mathematics Vol. 41; no. 1; pp. 211 - 232
Main Author: Garai, Gobinda
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.01.2024
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Approximation
Boundary conditions
Computational Mathematics and Numerical Analysis
Convergence
Decomposition
Energy
Mathematics
Mathematics and Statistics
Nonlinear equations
Nonlinearity
Numerical methods
Original Paper
65M15
Neumann–Neumann
Parallel computing
65M55
Domain decomposition
65Y05
Cahn–Hilliard equation
ISSN:0916-7005, 1868-937X
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-023-00600-y