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

Creative Commons License

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

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, cilt.18, sa.5, ss.303-314, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 5
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1515/ijnsns-2016-0024
  • Dergi Adı: INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.303-314
  • Anahtar Kelimeler: Cahn-Hilliard equation, gradient systems, discontinuous Galerkin method, average vector field method, VARIABLE-MOBILITY, MODELS, EFFICIENT, SYSTEMS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.