Analysis of a semi-implicit structure-preserving finite element method for the nonstationary incompressible magnetohydrodynamics equations. (English) Zbl 1452.76100
Summary: We revise the structure-preserving finite element method in [K. Hu et al., Numer. Math. 135, No. 2, 371–396 (2017; Zbl 1381.76174)]. The revised method is semi-implicit in time-discretization. We prove the linearized scheme preserves the divergence free property for the magnetic field exactly at each time step. Further, we showed the linearized scheme is unconditionally stable and we obtain optimal convergence in the energy norm of the revised method even for solutions with low regularity.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Citations:
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