A decoupled BDF2 numerical scheme is proposed and analyzed to solve the incompressible resistive magnetohydrodynamic (MHD) equations. In the numerical design, the pressure variable in the fluid field equation is computed through solving a Poisson equation, and a linear and decoupled method is adopted to separate both the magnetic and  the fluid field functions from the original system. The finite element method is used as the spatial discretization. As a result, the original system is divided into several sub-systems for which the numerical solutions can be obtained efficiently. The unique solvability, the unconditional energy stability, and particularly optimal error estimates will be theoretically established for the proposed scheme. Numerical results are presented to validate the theoretical results.

Dr. Cheng Wang is a professor in Department of  Mathematics at the University of Massachusetts Dartmouth (UMassD). He obtained his Ph.D degree from Temple University in 2000, under the supervision of  Prof. Jian-Guo Liu. Prior to joining UMassD in 2008 as an assistant professor, he was a Zorn postdoc at Indiana University from 2000 to 2003, under the supervision of Roger Temam and Shouhong Wang, and he worked as an assistant professor at University of Tennessee at Knoxville from 2003 to 2008. Dr. Wang’s research interests include development of stable, accurate numerical algorithms for partial differential equations and numerical analysis. He has published more than 80 papers with more than 3600 citations. He also serves in the Editorial Board of “Numerical Mathematics: Theory, Methods and Applications”.