An arbitrary-order discrete de Rham complex on polyhedral meshes. Part II: Consistency

In this paper we prove a complete panel of consistency results for the discrete de Rham (DDR) complex introduced in the companion paper https://hal.archives-ouvertes.fr/hal-03103526, including primal and adjoint consistency for the discrete vector calculus operators, and consistency of the corresponding potentials. The theoretical results are showcased by performing a full convergence analysis for a DDR approximation of a magnetostatics model. Numerical results on three-dimensional polyhedral meshes complete the exposition.

Daniele Antonio Di Pietro (1) , Jérôme Droniou (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 School of Mathematics [Australia]

Domaines: Analyse numérique [math.NA]

Daniele Antonio Di Pietro, Jérôme Droniou. An arbitrary-order discrete de Rham complex on polyhedral meshes. Part II: Consistency. 2021. ⟨hal-03103535⟩