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An efficient two-step algorithm for the stationary incompressible magnetohydrodynamic equations

Author

Listed:
  • Wu, Jilian
  • Liu, Demin
  • Feng, Xinlong
  • Huang, Pengzhan

Abstract

A new highly efficient two-step algorithm for the stationary incompressible magnetohydrodynamic equations is studied in this paper. The algorithm uses a lower order finite element pair (i.e., P1b−P1−P1) to compute an initial approximation, that is using the Mini-element (i.e., P1b−P1) to approximate the velocity and pressure and P1 element to approximate the magnetic field, then applies a higher order finite element pair (i.e., P2−P1−P2) to solve a linear system on the same mesh. Furthermore, the convergence analyses of standard Galerkin finite element method and the two-step algorithm are addressed. Lastly, numerical experiments are presented to verify both the theory and the efficiency of the algorithm.

Suggested Citation

  • Wu, Jilian & Liu, Demin & Feng, Xinlong & Huang, Pengzhan, 2017. "An efficient two-step algorithm for the stationary incompressible magnetohydrodynamic equations," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 21-33.
    • Handle: RePEc:eee:apmaco:v:302:y:2017:i:c:p:21-33
    DOI: 10.1016/j.amc.2017.01.005
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