Discrete vector potential representation of a divergence-free vector field in three-dimensional domains: numerical analysis of a model problem

François Dubois (1)

1 CMAP - Centre de Mathématiques Appliquées

For the representation of a divergence-free vector field defined on a bounded simply connected three-dimensional domain of with a smooth boundary by its curl and its normal component on the boundary, a mixed formulation also involving a vector potential is proposed. The vector fields are discretized with help of curved finite elements that are conforming in H(div) or H(curl). A discrete gauge condition is proposed to assume the uniqueness of the stream function. Optimal error estimates are derived, and a numerical experiment is presented.

Mots clés: mixed finite elements; curved boundaries; discrete gauge condition

Domaines: Analyse numérique [math.NA]

François Dubois. Discrete vector potential representation of a divergence-free vector field in three-dimensional domains: numerical analysis of a model problem. SIAM Journal on Numerical Analysis, 1990, 27 (5), pp.1103-1141. ⟨hal-00660366⟩