Vector-potential finite-element formulations for two-dimensional resistive magnetohydrodynamics

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-poten...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2019-01, Vol.77 (2), p.476-493
Main Authors: Adler, James H., He, Yunhui, Hu, Xiaozhe, MacLachlan, Scott P.
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Discretization
Finite element method
Formulations
Iterative methods
Magnetohydrodynamics
Mixed finite-element method
Newton’s method
Nonlinear equations
Two dimensional models
Well posed problems
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Summary: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2018.09.051