Stability and temporal error analysis for SAV schemes for electrohydrodynamic model with variable density

Abstract

In this paper, we construct and analyze first- and second-order schemes based on scalar auxiliary variable (SAV) approach for the electrohydrodynamic (EHD) model with variable density. These schemes only require solving a sequence of linear differential equations plus a linear well-posed algebraic equation at each time step, and are unconditionally energy stable. We carry out a rigorous error analysis for the first-order semi-discrete SAV scheme in two-dimensional case and derive the maximum principle, the optimal error estimates and the regularity estimates. Numerical experiments verify the accuracy and stability of the presented schemes.