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

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2017-08-01

Author

Sariaydin-Filibelioglu, Ayse
Karasözen, Bülent
Uzunca, Murat

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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.

Subject Keywords

Cahn–Hilliard equation, Gradient systems, Discontinuous Galerkin discretization, Average vector field method

URI

https://hdl.handle.net/11511/32352

Journal

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION

DOI

https://doi.org/10.1515/ijnsns-2016-0024

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

A. Sariaydin-Filibelioglu, B. Karasözen, and M. Uzunca, “Energy Stable Interior Penalty Discontinuous Galerkin Finite Element Method for Cahn-Hilliard Equation,” INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, pp. 303–314, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32352.