The flux-corrected-transport paradigm is generalized to implicit
finite element schemes and nonlinear systems of hyperbolic
conservation laws. In the scalar case, a nonoscillatory low-order
method of upwind type is derived by elimination of negative
off-diagonal entries of the discrete transport operator. The
difference between the discretizations of high and low order is
decomposed into a sum of skew-symmetric antidiffusive fluxes. An
iterative flux limiter independent of the time step is proposed for
implicit schemes. The nonlinear antidiffusion is incorporated into the
solution in the framework of a defect correction scheme preconditioned
by the monotone low-order operator. In the case of a hyperbolic
system, the global Jacobian matrix is assembled edge-by-edge without
resorting to numerical integration. Its low-order counterpart is
constructed by rendering all off-diagonal blocks positive definite or
adding scalar artificial diffusion proportional to the spectral radius
of the Roe matrix. The coupled equations are solved in a segregated
manner within an outer defect correction loop equipped with a
block-diagonal preconditioner. After a suitable synchronization, the
correction factors evaluated for an arbitrary set of indicator
variables are applied to the antidiffusive fluxes which are inserted
into the global defect vector. The performance of the new algorithm
is illustrated by numerical examples for scalar transport problems and
the compressible Euler equations.