Sharp Error Estimate of an Implicit BDF2 Scheme with Variable Time Steps for the Phase Field Crystal Model

摘要

Abstract A fully implicit two-step backward differentiation formula (BDF2) scheme with variable time steps is considered for solving the phase field crystal (PFC) model by combining with pseudo-spectral method in space. We show that the BDF2 scheme inherits a modified energy dissipation law under a mild ratio restriction A1, i.e., 0