TY - JOUR
TI - Energy-stable backward differentiation formula type fourier collocation spectral schemes for the Cahn-Hilliard equation
AU - Zhou Jun
AU - Cheng Ke-Long
JN - Thermal Science
PY - 2022
VL - 26
IS - 2
SP - 1095
EP - 1104
PT - Article
AB - 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.