Error Analysis of Euler Semi-implicit Scheme for the Nonstationary Magneto-hydrodynamics Problem with Temperature Dependent Parameters

Abstract

In this article we consider a fully discrete Euler semi-implicit scheme for the nonstationary electromagnetically and thermally driven flow, which is describing the motion of a nonisothermal incompressible magneto-hydrodyna-mics fluid subject to generalized Boussinesq problem with temperature dependent parameters. A prototypical time-stepping scheme, which is comprised of the Euler semi-implicit discretization in time and conforming mixed finite element approximation in space is studied in detail. We obtain that the proposed scheme is unconditionally stable and derive some optimal error estimates for the fluid velocity, the fluid magnetic and the fluid temperature. Moreover, a suboptimal error estimate for the fluid pressure is proved. Numerical results are provided to verify the theoretical rates of the scheme.