Two-level Picard coupling correction finite element method based on charge-conservation for stationary inductionless magnetohydrodynamic equations. (1st June 2022)

• Record Type: Journal Article
• Authors: Zhou, Xianghai; Su, Haiyan; Tang, Bo
• Is Part Of: Computers & mathematics with applications. Volume 115(2022)
• Page Start: 41
• Page End: 56
• Publication Date: 2022-06-01
• Subjects: Inductionless MHD equations -- Two-level -- Finite element method -- Picard coupling correction -- Error estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.04.004
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we propose two two-level finite element methods based on charge-conservation to solve the 2D/3D stationary inductionless magnetohydrodynamic (MHD) equations in Lipschitz domain. The methods are based on the Picard coupling correction on the fine mesh, one has to solve a nonlinear problem on the coarse mesh, the other one need to solve a linearized problem with Newton iteration on the coarse mesh. In addition, we give the stabilities and error estimates for the proposed methods. Several numerical results are presented to verify the theoretical analysis and show the effectiveness of the methods.