  We study a framework that allows to solve the coarse problem in the FETI-DP
method approximately. It is based on the saddle-point formulation of the
FETI-DP system with a block-triangular preconditioner. One of the blocks
approximates the coarse problem, for which we use the multilevel BDDC method as
the main tool. This strategy then naturally leads to a version of multilevel
FETI-DP method, and we show that the spectra of the multilevel FETI-DP and BDDC
preconditioned operators are essentially the same. The theory is illustrated by
a set of numerical experiments, and we also present a few experiments when the
coarse solve is approximated by algebraic multigrid.
