The Virtual Element Method for the 3D Resistive Magnetohydrodynamic model

Lourenço Beirão da Veiga, Franco Dassi, Gianmarco Manzini, Lorenzo Mascotto

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.

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