Unconditional stability and optimal error estimates of first order semi-implicit stabilized finite element method for two phase magnetohydrodynamic diffuse interface model

Abstract

This paper is devoted to present the rigorous unconditional stability and optimal error estimates of first order semi-implicit energy stable finite element method developed by Yang et al. (Comput. Methods Appl. Mech. Engrg. 356 (2019) 435–464) for the two phase magnetohydrodynamic(MHD) flows, some numerical results are also provided to show the performances of the considered numerical scheme.