Abstract This paper introduces a novel approach to analyze two-level overlapping Schwarz methods for Nédélec and Raviart–Thomas vector field problems. The theory is based on new regular stable decompositions for vector fields that are robust to the topology of the domain. Enhanced estimates for the condition numbers of the preconditioned linear systems are derived, dependent linearly on the relative overlap between the overlapping subdomains. Furthermore, we present the numerical experiments which support our theoretical results.
Oh et al. (Tue,) studied this question.