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Journal Articles Mathematical Models and Methods in Applied Sciences Year : 2022

A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics

Abstract

We prove a discrete version of the first Weber inequality on three-dimensional hybrid spaces spanned by vectors of polynomials attached to the elements and faces of a polyhedral mesh. We then introduce two Hybrid High-Order methods for the approximation of the magnetostatics model, in both its (first-order) field and (second-order) vector potential formulations. These methods are applicable on general polyhedral meshes, and allow for arbitrary orders of approximation. Leveraging the previously established discrete Weber inequality, we perform a comprehensive analysis of the two methods. We finally validate them on a set of test-cases.
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Dates and versions

hal-02892526 , version 1 (07-07-2020)
hal-02892526 , version 2 (14-06-2021)
hal-02892526 , version 3 (24-10-2021)

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Florent Chave, Daniele Antonio Di Pietro, Simon Lemaire. A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics. Mathematical Models and Methods in Applied Sciences, 2022, 32 (1), pp.175-207. ⟨10.1142/S0218202522500051⟩. ⟨hal-02892526v3⟩
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