A consistent projection finite element method for the non-stationary incompressible thermally coupled MHD equations.

This paper introduces a consistent projection finite method for the non-stationary incompressible thermally coupled MHD equations, which buoyancy affects because temperature differences in the flow cannot be neglected. It is a fully discrete projection method. The unconditional stability and error estimates of the velocity, pressure, temperature, and magnetic field under some assumptions are given. Then some numerical experiments are prescribed to support the effectiveness of the consistent projection finite element method. • A consistent projection finite method for thermally coupled MHD equations is given. • The buoyancy affects because temperature differences in the flow are considered. • It is a fully discrete projection method. • The unconditional stability and error estimates under some assumptions are given. [ABSTRACT FROM AUTHOR]