An high-accuracy energy stable numerical scheme for the phase field crystal equation

Abstract:

In this paper, we propose an energy stable numerical scheme for the phase field crystal equation with periodic boundary condition. This scheme is based on the structure of the energy functional. A Fourier pesudo spectral approximation is applied in space as well as a third order backward differentiation scheme is applied in the temporal approximation for the equation. Meanwhile, a Douglas-Dupont type regularization term is added to ensure the modified energy stability. The unique solvability and energy stability of the scheme are established. Finally, some numerical examples are presented to confirm the robustness and accuracy of the scheme.