A FETI domain decomposition method for edge element approximations in two dimensions with discontinuous coefficients

A class of finite element tearing and interconnecting (FETI) methods for th e edge element approximation of vector field problems in two dimensions is introduced and analyzed. First, an abstract framework is presented for the analysis of a class of FETI methods where a natural coarse problem, associa ted with the substructures, is lacking. Then, a family of FETI methods for edge element approximations is proposed. It is shown that the condition num ber of the corresponding method is independent of the number of substructur es and grows only polylogarithmically with the number of unknowns associate d with individual substructures. The estimate is also independent of the ju mps of both of the coefficients of the original problem. Numerical results validating our theoretical bounds are given. The method and its analysis ca n be easily generalized to Raviart-Thomas element approximations in two and three dimensions.