New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamics

作者：Gao, Huadong; Qiu, Weifeng^*; Sun, Weiwei

来源：Numerische Mathematik, 2023, 153(2-3): 327-358.

DOI：10.1007/s00211-022-01341-9

• 65N30
• 65L12

This paper focuses on a new error analysis and a recovering technique of frequently-used mixed FEMs for a dynamical incompressible magnetohydrodynamics (MHD)system. The methods use the standard inf-sup stable Taylor-Hood/MINI velocity-pressure space pairs to solve the Navier-Stokes equations and the Nedelec's edgeelement for solving the magnetic field. We establish new and optimal error estimates.In particular, we prove that the method provides the optimal accuracy for the MINIelement inL2-norm and for the Taylor-Hood element inH1-norm. The analysis isbased on a modified Maxwell projection and the corresponding estimates in negativenorms, while all the existing analysis is not optimal due to the strong coupling ofsystem and the pollution of the lower-order Nedelec's edge approximation in analy-sis. In addition, at any given time step, we develop a simple recovery technique fornumerical approximation to the magnetic field of one order higher accuracy in thespatial direction.

• 单位
  华中科技大学