Résumé
In this paper we prove a complete panel of consistency results for the
discrete de Rham (DDR) complex introduced in the companion paper [D. A. Di
Pietro and J. Droniou, An arbitrary-order discrete de Rham complex on
polyhedral meshes. Part I: Exactness and Poincaré inequalities, 2021,
submitted], 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.