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

Jilian Wu, Demin Liu, Xinlong Feng and Pengzhan Huang

Applied Mathematics and Computation, 2017, vol. 302, issue C, 21-33

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.

Keywords: Stationary incompressible magnetohydrodynamic equations; Two-step algorithm; Finite element method; Convergence analyses (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:302:y:2017:i:c:p:21-33

DOI: 10.1016/j.amc.2017.01.005

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