seminar

In this talk, I will present some recent studies on second-order stabilized linear semi-implicit numerical schemes for the nonlocal Cahn-Hilliard equation, a variant of the classic Cahn-Hilliard equation with a Laplacian replaced by a nonlocal diffusion operator. By applying the explicit extrapolation to the nonlinear term and adding appropriate stabilization terms, the resulting constant-coefficient linear schemes bring great numerical convenience, while the theoretical analysis becomes very challenging due to the lack of high-order diffusion. Resorting to the higher-order consistency estimate for the numerical schemes, we conduct the complete convergence analysis, containing the rough and refined error estimates, and justify the discrete L-infinity bound of the numerical solution as a byproduct. Moreover, the energy stability is also obtained with respect to a modified energy. Numerical experiments are conducted for a typical case involving Gaussian kernels, including the comparison between the nonlocal and local phase transitions and the long-time simulations of the coarsening dynamics.