Linear and unconditionally energy stable schemes for the modified phase field crystal equation

Abstract

In this paper, two temporal discrete numerical schemes of the modified phase field crystal equation are presented by introducing a Lagrange multiplier U and two auxiliary functions ψ, W, which reduce the order of the original equation in time and space. For these schemes, we prove their mass conservation and energy stability. Error estimates of the BDF2 scheme are given. In the end, some numerical experiments are used to verify the correctness of our theoretical results.