Dual-Primal Feti Algorithms for Edge Element Approximations: Two-Dimensional H and P Finite Elements on Shape-Regular Meshes

A family of dual-primal finite element tearing and interconnecting (FETI) methods for edge element approximations in two dimensions is proposed and analyzed. The primal constraints here are averages over subdomain edges. It is shown that the condition number of the corresponding method is independent of the number of substructures and grows only polylogarithmically with the number of unknowns associated with individual substructures. The estimate is also independent of the jumps of both of the coefficients of the original problem. Numerical results validating our theoretical bounds are given.