Energy Preserving Discretization of the Nonlinear Schödinger Equation by Interior Penalty Discontinuous Galerkin Method

Date

2015-09-14

Author

Karasözen, Bülent

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http://enumath2015.iam.metu.edu.tr/bookOfAbstracts.pdf
https://hdl.handle.net/11511/80667

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Energy Stable Interior Penalty Discontinuous Galerkin Finite Element Method for Cahn-Hilliard Equation Sariaydin-Filibelioglu, Ayse; Karasözen, Bülent; Uzunca, Murat (2017-08-01) 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 ...
Energy Stable Discontinuous Galerkin Finite Element Method for the Allen-Cahn Equation Karasözen, Bülent; Sariaydin-Filibelioglu, Ayse; Yücel, Hamdullah (2018-05-01) In this paper, we investigate numerical solution of Allen-Cahn equation with constant and degenerate mobility, and with polynomial and logarithmic energy functionals. We discretize the model equation by symmetric interior penalty Galerkin (SIPG) method in space, and by average vector field (AVF) method in time. We show that the energy stable AVF method as the time integrator for gradient systems like the Allen-Cahn equation satisfies the energy decreasing property for fully discrete scheme. Numerical result...

Citation Formats

B. Karasözen, “Energy Preserving Discretization of the Nonlinear Schödinger Equation by Interior Penalty Discontinuous Galerkin Method,” 2015, Accessed: 00, 2021. [Online]. Available: http://enumath2015.iam.metu.edu.tr/bookOfAbstracts.pdf.