An arbitrary-order discontinuous skeletal method for solving electrostatics on general polyhedral meshes

Daniele Antonio Di Pietro (1) , Bernard A Kapidani (2) , Ruben A Specogna (2) , Francesco A Trevisan (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Dipartimento Politecnico di Ingegneria e Architettura

We present a numerical method named Mixed High Order (MHO) to obtain high order of convergence for electrostatic problems solved on general polyhedral meshes. The method, based on high-order local reconstructions of differential operators from face and cell degrees of freedom, exhibits a moderate computational cost thanks to hybridization and static condensation that eliminate cell unknowns. After surveying the method, we first assess its effectiveness for three-dimensional problems by comparing for the first time its performances with classical conforming finite elements. Moreover, we emphasize the algebraic equivalence of MHO in the lowest-order with the analog formulation obtained with the Discrete Geometric Approach or the Finite Integration Technique.

Mots clés: Poisson problem; Hybrid High-Order; Electrostatics; Mixed High-Order; Polyhedral meshes

Domaines: Analyse numérique [math.NA]

Daniele Antonio Di Pietro, Bernard A Kapidani, Ruben A Specogna, Francesco A Trevisan. An arbitrary-order discontinuous skeletal method for solving electrostatics on general polyhedral meshes. IEEE Transactions on Magnetics, 2017, 53 (6), pp.1-4. ⟨10.1109/TMAG.2017.2666546⟩. ⟨hal-01399505⟩