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


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Sariaydin-Filibelioglu A., KARASÖZEN B., Uzunca M.

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, vol.18, no.5, pp.303-314, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.1515/ijnsns-2016-0024
  • Journal Name: INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.303-314
  • Keywords: Cahn-Hilliard equation, gradient systems, discontinuous Galerkin method, average vector field method, VARIABLE-MOBILITY, MODELS, EFFICIENT, SYSTEMS
  • Middle East Technical University Affiliated: Yes

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.