The virtual element method for the 3D resistive magnetohydrodynamic model

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.

Automated summary

We propose a four-field virtual element discretization method for the time-dependent resistive magnetohydrodynamics equations in three dimensions, with a focus on the semi-discrete formulation. This method utilizes general polyhedral meshes and ensures divergence-free velocity and magnetic fields up to machine precision. We provide a comprehensive convergence analysis under appropriate regularity assumptions, which is supported by numerical tests.