| Abstract: |
| In this talk, we present a new error analysis of a class of fully discrete finite element methods for the dynamical inductionless magnetohydrodynamic equations. The methods use the semi- implicit backward Euler scheme in time and use the standard inf-sup stable Mini/Taylor-Hood pairs to discretize the velocity and pressure, and the Raviart-Thomas for solving the current density in space. Due to the strong coupling of the system and the pollution of the lower-order Raviart-Thomas face approximation in analysis, the existing analysis is not optimal. In terms of a mixed Poisson projection and the corresponding estimates in negative norms, we establish new and optimal error estimates for all variables. Numerical experiments are performed to verify the theoretical analysis. |
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