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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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IMPACT FACTOR 2017: 1.162

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2191-0294
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Volume 18, Issue 5

Issues

Energy Stable Interior Penalty Discontinuous Galerkin Finite Element Method for Cahn–Hilliard Equation

Ayşe Sarıaydın-Filibelioğlu
  • Corresponding author
  • Econometry Department, 100. Yıl University, Van, Turkey
  • Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Bülent Karasözen
  • Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey
  • Department of Mathematics, Middle East Technical University, Ankara, Turkey
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Murat Uzunca
Published Online: 2017-07-14 | DOI: https://doi.org/10.1515/ijnsns-2016-0024

Abstract

An energy stable conservative method is developed for the Cahn–Hilliard (CH) equation with the degenerate mobility. The CH equation is discretized in space with the mass conserving symmetric interior penalty discontinuous Galerkin (SIPG) method. The resulting semi-discrete nonlinear system of ordinary differential equations are solved in time by the unconditionally energy stable average vector field (AVF) method. We prove that the AVF method preserves the energy decreasing property of the fully discretized CH equation. Numerical results for the quartic double-well and the logarithmic potential functions with constant and degenerate mobility confirm the theoretical convergence rates, accuracy and the performance of the proposed approach.

Keywords: Cahn–Hilliard equation; gradient systems; discontinuous Galerkin method; average vector field method

JEL Classification: 02.60.Cb; 02.60.Lj; 02.70.Dh

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About the article

Received: 2016-02-11

Accepted: 2017-05-04

Published Online: 2017-07-14

Published in Print: 2017-07-26


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 18, Issue 5, Pages 303–314, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2016-0024.

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