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Analysis of a new mixed FEM for stationary incompressible magneto-hydrodynamics.
- Source :
-
Computers & Mathematics with Applications . Dec2022, Vol. 127, p65-79. 15p. - Publication Year :
- 2022
-
Abstract
- In this paper we propose and analyze a new mixed finite element method for a stationary magneto-hydrodynamic (MHD) model. The method is based on the utilization of a new dual-mixed formulation recently introduced for the Navier-Stokes problem, which is coupled with a classical primal formulation for the Maxwell equations. The latter implies that the velocity and a pseudostress tensor relating the velocity gradient with the convective term for the hydrodynamic equations, together with the magnetic field and a Lagrange multiplier related with the divergence-free property of the magnetic field, become the main unknowns of the system. Then the associated Galerkin scheme can be defined by employing Raviart–Thomas elements of degree k for the aforementioned pseudostress tensor, discontinuous piecewise polynomial elements of degree k for the velocity, Nédélec elements of degree k for the magnetic field and Lagrange elements of degree k for the associated Lagrange multiplier. The analysis of the continuous and discrete problems are carried out by means of the Lax–Milgram lemma, the Banach–Nečas–Babuška and Banach fixed-point theorems, under a sufficiently small data assumption. In particular, the analysis of the discrete scheme requires a quasi-uniformity assumption on mesh. We also develop an a priori error analysis and show that the proposed finite element method is optimal convergent. Finally, some numerical results illustrating the good performance of the method are provided. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08981221
- Volume :
- 127
- Database :
- Academic Search Index
- Journal :
- Computers & Mathematics with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 160315430
- Full Text :
- https://doi.org/10.1016/j.camwa.2022.09.017