A two-derivative time integrator for the Cahn-Hilliard equation

This paper presents a two-derivative energy-stable method for the Cahn-Hilliard equation. We use a fully implicit time discretization with the addition of two stabilization terms to maintain the energy stability. As far as we know, this is the first time an energy-stable multiderivative method has b...

Full description

Saved in:
Bibliographic Details
Published inMathematical modelling and analysis Vol. 29; no. 4; pp. 714 - 730
Main Authors Theodosiou, Eleni, Bringedal, Carina, Schütz, Jochen
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 22.11.2024
Subjects
Accuracy
Analysis
Cahn-Hilliard equation
Energy
energy-stable methods
high-order methods
Mathematical analysis
Methods
multiderivative methods
Numerical analysis
Ordinary differential equations
Predictor-corrector methods
Cahn-Hilliard equation
multiderivative methods
energy-stable methods
high-order methods
Online AccessGet full text
ISSN1392-6292
1648-3510
1648-3510
DOI10.3846/mma.2024.20646

Cover

More Information
Summary:This paper presents a two-derivative energy-stable method for the Cahn-Hilliard equation. We use a fully implicit time discretization with the addition of two stabilization terms to maintain the energy stability. As far as we know, this is the first time an energy-stable multiderivative method has been developed for phase-field models. We present numerical results of the novel method to support our mathematical analysis. In addition, we perform numerical experiments of two multiderivative predictor-corrector methods of fourth and sixth-order accuracy, and we show numerically that all the methods are energy stable.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1392-6292
1648-3510
1648-3510
DOI:10.3846/mma.2024.20646