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

Florent Chave (1) , Daniele Antonio Di Pietro (2) , Simon Lemaire (1)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 IMAG - Institut Montpelliérain Alexander Grothendieck

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.

Mots clés: Weber inequalities; Hybrid spaces; Polyhedral meshes; Hybrid High-Order methods; Magnetostatics

Domaines: Analyse numérique [math.NA]

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⟩