1. Robust globally divergence-free Weak Galerkin finite element method for incompressible Magnetohydrodynamics flow.
- Author
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Zhang, Min, Zhang, Tong, and Xie, Xiaoping
- Subjects
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INCOMPRESSIBLE flow , *FINITE element method , *GALERKIN methods , *MAGNETIC fields , *GLOBAL analysis (Mathematics) , *MAGNETOHYDRODYNAMICS - Abstract
This paper develops a weak Galerkin (WG) finite element method of arbitrary order for the steady incompressible Magnetohydrodynamics equations. The WG scheme uses piecewise polynomials of degrees k (k ≥ 1) , k , k − 1 and k − 1 respectively for the approximations of the velocity, the magnetic field, the pressure, and the magnetic pseudo-pressure in the interior of elements, and uses piecewise polynomials of degree k for their numerical traces on the interfaces of elements. The method is shown to yield globally divergence-free approximations of the velocity and magnetic fields. We give existence and uniqueness results for the discrete scheme and derive optimal a priori error estimates. We also present a convergent linearized iterative algorithm. Numerical experiments are provided to verify the obtained theoretical results. • We develop a weak Galerkin method of arbitrary order for the steady incompressible MHD equations. • The method is shown to yield globally divergence-free approximations of the velocity and magnetic fields. • We give existence and uniqueness results for the discrete scheme and derive optimal a priori error estimates. • We also present a convergent linearized iterative algorithm. • Numerical experiments confirm the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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