The Virtual Element Method for the 3D Resistive Magnetohydrodynamic model

01/12/2022

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by   Lourenco Beirao da Veiga, et al.

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We present a four-field Virtual Element discretization for the time-dependent resistive Magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete formulation. The proposed method employs general polyhedral meshes and guarantees velocity and magnetic fields that are divergence free up to machine precision. We provide a full convergence analysis under suitable regularity assumptions, which is validated by some numerical tests.