Energy stable interior penalty discontinuous Galerkin finite element method for Cahn-Hilliard equation
Provides a provably energy-stable and mass-conserving numerical scheme for a specific PDE, which is incremental for the computational PDE community.
The authors developed an energy stable conservative numerical method for the Cahn-Hilliard equation with degenerate mobility, combining SIPG spatial discretization with AVF time integration. Numerical results confirm theoretical convergence rates and energy stability.
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 CH equation. Numerical results confirm the theoretical convergence rates and the performance of the proposed approach.