Dual-primal FETI algorithms for edge finite-element approximations in 3D

A family of dual-primal finite-element tearing and interconnecting methods for edge-element approximations in 3D is proposed and analysed. The key part of this work relies on the observation that for these finite-element spaces there is a strong coupling between degrees of freedom associated with subdomain edges and faces and a local change of basis is therefore necessary. The primal constraints are associated with subdomain edges. We propose three methods. They ensure a condition number that is independent of the number of substructures and possibly large jumps of one of the coefficients of the original problem, and only depends on the number of unknowns associated with a single substructure, as for the corresponding methods for continuous nodal elements. A polylogarithmic dependence is shown for two algorithms. Numerical results validating our theoretical bounds are given.