Remarks on the asymptotic behavior of scalar auxiliary variable (SAV) schemes for gradientlike flows 
Anass Bouchriti,Morgan Pierre,Nour Eddine Alaa 
Keywords:gradient flow, SAV schemes, AllenCahn equation, CahnHilliard equation, sineGordon equation 
Abstract: 
We introduce a time semidiscretization of a damped wave equation by a SAV scheme with second order accuracy. The energy dissipation law is shown to hold without any restriction on the time step. We prove that any sequence generated by the scheme converges to a steady state (up to a subsequence). We notice that the steady state equation associated to the SAV scheme is a modified version of the steady state equation associated to the damped wave equation. We show that a similar result holds for a SAV fully discrete version of the CahnHilliard equation and we compare numerically the two steady state equations. 



