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

摘要

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-infinity(0, +infinity; L-infinity(Omega)) 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. (C) 2018 Elsevier Ltd. All rights reserved.