A Voigt regularization of the thermally coupled magnetohydrodynamic flow

We prove existence and uniqueness of weak solution to a Voigt regularization of the three-dimensional thermally coupled MHD equations. Moreover, for the considered equations, we propose a fully discrete scheme that has unconditional stability and is convergent. All computational results support the theoretical analysis and show the effect of the Voigt regularization on the thermally coupled magnetohydrodynamic flow.