Vector-potential finite-element formulations for two-dimensional resistive magnetohydrodynamics. (15th January 2019)

• Record Type: Journal Article
• Authors: Adler, James H.; He, Yunhui; Hu, Xiaozhe; MacLachlan, Scott P.
• Is Part Of: Computers & mathematics with applications. Volume 77:issue 2(2019)
• Page Start: 476
• Page End: 493
• Publication Date: 2019-01-15
• Subjects: Magnetohydrodynamics -- Mixed finite-element method -- Newton's method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.09.051
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Vector-potential formulations are attractive for electromagnetic problems in two dimensions, since they reduce both the number and complexity of equations, particularly in coupled systems, such as magnetohydrodynamics (MHD). In this paper, we consider the finite-element formulation of a vector-potential model of two-dimensional resistive MHD. Existence and uniqueness are considered separately for the continuum nonlinear equations and the discretized and linearized form that arises from Newton's method applied to a modified system. Under some conditions, we prove that the solutions of the original and modified weak forms are the same, allowing us to prove convergence of the discretization and well-posedness of the nonlinear iteration near a solution.