It is well known that the vector finite element method is one of the powerful tools for solving electromagnetic problems. The vector shape functions that are consist of the facet and the edge vector shape functions have a lot of characteristics. One of them is automatic conservation of the magnetic flux density in analyzing the Induction equations without iterative correction. In the present paper the vector finite element method is applied to the problems of magnetohydrodynamics. Three-dimensional natural convection in a cavity under a constant magnetic field is analyzed numerically using the GSMAC finite element method for flow field and temperature field and the vector finite element method for the Induction equations. The computational results are good agreement with those obtained using B method that is one of the iterative methods to satisfy the solenoidal condition for the magnetic flux density of the Induction equations.

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