Open AccessEnergy-stable backward differentiation formula type fourier collocation spectral schemes for the Cahn-Hilliard equation
Author(s) -
Zhou Jun,
Kelong Cheng
Publication year - 2022
Publication title -
thermal science/thermal science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.339
H-Index - 43
eISSN - 2334-7163
pISSN - 0354-9836
DOI - 10.2298/tsci2202095z
Subject(s) - discretization , regularization (linguistics) , collocation (remote sensing) , stencil , spectral method , fourier transform , mathematics , term (time) , mathematical analysis , physics , computer science , computational science , quantum mechanics , machine learning , artificial intelligence
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.