Stability and temporal error estimate of scalar auxiliary variable schemes for the magnetohydrodynamics equations with variable density

In this article, we construct first‐ and second‐order semidiscrete schemes for the magnetohydrodynamics (MHD) equations with variable density based on scalar auxiliary variable (SAV) approach. These schemes are decoupled, unconditionally energy stable and only solve a sequence of linear differential equations at each time step. We carry out a rigorous error analysis for the first‐order SAV scheme in two‐dimensional case. Some numerical experiments are presented to verify the accuracy and stability.