2023/10/05 by Min Zhang, Tong Zhang, Zhang, Min +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2310.03247
openalex publication_date 2023/10/05 · openalex created_date 2023/10/09 · openalex updated_date 2026/07/28
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.