Energy-stable backward differentiation formula type fourier collocation spectral schemes for the Cahn-Hilliard equation

Abstract

We present a variant of second order accurate in time backward differentiation formula schemes for the Cahn-Hilliard equation, with a Fourier collocation spectral approximation in space. A three-point stencil is applied in the temporal discretization, and the concave term diffusion term is treated explicitly. An addition-al Douglas-Dupont regularization term is introduced, which ensures the energy stability with a mild requirement. Various numerical simulations including the verification of accuracy, coarsening process and energy decay rate are presented to demonstrate the efficiency and the robustness of proposed schemes.