4.6 Article

The virtual element method for the 3D resistive magnetohydrodynamic model

Journal

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 33, Issue 3, Pages 643-686

Publisher

WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S021820252350015X

Keywords

Resistive magnetohydrodynamics; Navier-Stokes equations; Maxwell's equations; virtual element method; polyhedral meshes

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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.
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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