The flux-corrected transport (FCT) methodology is generalized to
implicit finite element schemes and applied to the Euler equations of
gas dynamics. The underlying low-order scheme is constructed by
applying scalar artificial viscosity proportional to the spectral
radius of the cumulative Roe matrix.  All conservative matrix
manipulations are performed edge-by-edge which leads to an efficient
algorithm for the matrix assembly. The outer defect correction loop is
equipped with a block-diagonal preconditioner so as to decouple the
discretized Euler equations and solve all equations individually. As
an alternative, a strongly coupled solution strategy is investigated
in the context of stationary problems which call for large time steps.