Unconditional stability and error estimates of the modified characteristics FEMs for the time-dependent incompressible MHD equations

Abstract

This paper focuses on the unconditional stability and convergence of characteristics type methods for the time-dependent incompressible MHD equations. For this purpose, we introduce a new characteristics time-discrete system. The optimal error estimates in L2 and H1 norms for the typical modified characteristics finite element method unconditionally can be deduced, while the whole previous works require certain time-step restrictions. Some numerical experiments document performance of the characteristics type methods for the time-dependent incompressible MHD equations.