Stability and convergence of semi-implicit time-stepping algorithm for stationary incompressible magnetohydrodynamics

Abstract

For the stationary incompressible magnetohydrodynamics (MHD) equations, we provide a new uniqueness assumption (A0) and show the exponential stability of the solution. Then, the semi-implicit time-stepping algorithm is used to solve the stationary MHD equations. The algorithm is proved to be unconditionally stable. The discrete velocity and magnetic field are bounded in L∞(0,+∞;L∞(Ω)) for any space and time step sizes. The error estimates for the algorithm are deduced under the uniqueness conditions. Finally, numerical experiments are performed to testify our theoretical analysis.