Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system

In this paper, we focus on pressure-robust analysis of a mixed finite element method for the numerical discretization of nonstationary magnetohydrodynamics system. The velocity field is discretized by divergence-conforming Raviart-Thomas spaces with interior penalties, and the magnetic equation is approximated by curl-conforming Nedelec edge elements. The main feature of the method is that it produces exactly divergence-free velocity approximation, and captures the strongest magnetic singularities. The results show that the proposed scheme meets a discrete unconditional energy stability and the numerical solution is well-posedness. In addition, a priori error estimates are given, in which the constants are independent of the Reynolds number. Finally, we provide several numerical results illustrating the good performance of the scheme and confirming the theoretical rates of convergence.

Automated summary

In this paper, a mixed finite element method is proposed to robustly analyze the pressure problem in nonstationary magnetohydrodynamics system. The method features divergence-free velocity approximation and capturing the strongest magnetic singularities. The results demonstrate the scheme's energy stability and well-posedness of the numerical solution, along with a priori error estimates independent of the Reynolds number.