A consistent projection finite element method for the incompressible MHD equations. Issue 12 (10th September 2021)

• Record Type: Journal Article
• Authors: Yang, Yang; Si, Zhiyong
• Is Part Of: Applicable analysis. Volume 100:Issue 12(2021)
• Page Start: 2606
• Page End: 2626
• Publication Date: 2021-09-10
• Subjects: Incompressible MHD equations -- consistent projection method -- finite element method -- optimal error estimates; 76D05 -- 35Q30 -- 65M60 -- 65N30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1695782
• Languages: English
• ISSNs: 0003-6811

Abstract

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.