Error estimates for second-order SAV finite element method to phase field crystal model

Abstract

<p style='text-indent:20px;'>In this paper, the second-order scalar auxiliary variable approach in time and linear finite element method in space are employed for solving the Cahn-Hilliard type equation of the phase field crystal model. The energy stability of the fully discrete scheme and the boundedness of numerical solution are studied. The rigorous error estimates of order <inline-formula><tex-math id="M1">$ O(\tau^2+h^2) $</tex-math></inline-formula> in the sense of <inline-formula><tex-math id="M2">$ L^2 $</tex-math></inline-formula>-norm is derived. Finally, some numerical results are given to demonstrate the theoretical analysis.</p>