A consistent projection finite element method for the incompressible MHD equations

ABSTRACT

In this paper, we introduce a consistent projection finite element method for the impressible MHD (MagnetoHydroDynamics) equations. It's a fully discrete projection method, which associates the virtues of both the gauge and Uzawa methods with a variational framework. We also testify the unconditional stability and error estimates of the velocity, pressure and magnetic field by the variational method using some assumptions. Finally, we present some numerical experiments to support the validity of the consistent projection finite element method.

KEYWORDS:

• Incompressible MHD equations
• consistent projection method
• finite element method
• optimal error estimates

AMS SUBJECT CLASSIFICATIONS:

• 76D05
• 35Q30
• 65M60
• 65N30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the author was supported in part by the NSF of China [grant number 11401177].