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Error analysis of a fully discrete PFEM for the 2D/3D unsteady incompressible MHD equations

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  • Shi, Kaiwen
  • Su, Haiyan
  • Feng, Xinlong

Abstract

The aim of this article is to present a penalty finite element method (PFEM) in fully discrete form for the unsteady incompressible magnetohydrodynamic (MHD) equations. The proposed method is applied to address the incompressible constraint “divv=0”. The backward Euler scheme is used for temporal discretization, and the (P1b,P1,P1) finite element pair is used for spatial discretization, which satisfies the discrete LBB condition. Moreover, rigorous analysis of the optimal error estimate for the fully discrete PFEM is provided, which depends on penalty parameter ϵ, the mesh size h and the time step size Δt. Finally, some benchmark numerical experiments which include the hydromagnetic Kelvin-Helmholtz instability, flow around a cylinder and lid driven cavity flow, are carried out to illustrate the theoretical results and the effectiveness of the our proposed method.

Suggested Citation

  • Shi, Kaiwen & Su, Haiyan & Feng, Xinlong, 2024. "Error analysis of a fully discrete PFEM for the 2D/3D unsteady incompressible MHD equations," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    • Handle: RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003205
    DOI: 10.1016/j.amc.2024.128859
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