报告地点：行健楼学术报告厅526
邀请人：汪艳秋教授
摘要：We present a second order accurate (in time) backward differentiation formula energy stable numerical scheme for the Cahn-Hilliard equation, with a mixed finite element approximation in space. Instead of the standard second order Crank-Nicolson methodology, we apply the BDF concept to derive the second order temporal accuracy, with a
modification as taking a second order accurate, explicit treatment for the concave diffusion term. An explicit treatment is kept for the
concave part of the chemical potential, so that a unique solvability is assured. A second order Douglas-Dupont-type regularization is added, and a careful calculation shows that energy stability is guaranteed. In
turn, a uniform in time H^1 bound of the numerical solution becomes available. As a result, we are able to establish the convergence
analysis for the proposed fully discrete scheme, with full O (\tau^2 + h^2) accuracy. This convergence turns out to be unconditional; no
scaling law is needed between the time step size and the spatial grid size.