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The two-level element free Galerkin method for MHD flow at high Hartmann numbers. (English) Zbl 1223.76128
Summary: A new element free Galerkin method, namely the two-level element free Galerkin method, is presented for solving the governing equations of steady magnetohydrodynamic duct flow. Because this element free Galerkin method makes use of the nodal point configurations which do not require a mesh, it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometric problems. Another distinguished feature of the proposed method is the resolving capability of high gradients near the layer regions without local or adaptive refinements. Numerical results indicate that, no matter how large the Hartmann number is, this method has the ability to produce satisfactory results for the velocity and the magnetic field simultaneously. That is to say, the presented method has some excellent properties such as better stability and accuracy.

##### MSC:
 76W05 Magnetohydrodynamics and electrohydrodynamics 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 76M12 Finite volume methods applied to problems in fluid mechanics 65Z05 Applications to the sciences 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
Mfree2D
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