An approximate factorization/least squares solution method for a mixed finite element approximation of the Cahn-Hilliard equation
type: Item
instance of: scholarly article
title: An approximate factorization/least squares solution method for a mixed finite element approximation of the Cahn-Hilliard equation
zbMATH Open document ID: 0874.65073
DOI: 10.1007/BF03167260
author: D. A. Trevas
author: Edward Dean
author: Roland Glowinski
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 1997-11-02T00:00:00Z
review text: This paper deals with the numerical solution of the Cahn-Hilliard equation. A mixed formulation making possible the approximation of the problem \[ \frac{\partial u}{\partial t}- \Delta(u^3-u)+ \varepsilon^2\Delta^2u=0 \quad\text{in }\Omega\times (0,T), \] \[ u(x,0)= u_0(x), \quad x\in\Omega, \quad \frac{\partial u}{\partial n}=\frac{\partial}{\partial n}\Delta u=0\quad\text{on }\partial\Omega, \] by finite element techniques traditionally used for the approximation of second-order elliptic or parabolic problems is combined with a least squares formulation based on an approximate factorization of a fourth-order elliptic operator which appears in the numerical model. The authors have visualized the computed solutions of two problems to illustrate the possibilities of the presented methods.
reviewed by: Pavol Chocholatý
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1000125
zbMATH Keywords: least squares method
zbMATH Keywords: Cahn-Hilliard equation
zbMATH Keywords: finite element
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03167260
OpenAlex ID: W1998178242
description: scientific article; zbMATH DE number 1000125