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An arbitrary-order discrete de Rham complex on polyhedral meshes. Part II: Consistency (2101.04946v2)
Published 13 Jan 2021 in math.NA and cs.NA
Abstract: 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 Poincar\'e 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.