A new generalization of the flux-corrected transport (FCT)
  methodology to implicit finite element discretizations is proposed.
  The underlying high-order scheme is supposed to be unconditionally
  stable and produce time-accurate solutions to evolutionary
  convection problems. Its nonoscillatory low-order counterpart is
  constructed by means of mass lumping followed by elimination of
  negative off-diagonal entries from the discrete transport operator.
  The raw antidiffusive fluxes, which represent the difference between
  the high- and low-order schemes, are updated and limited within an
  outer fixed-point iteration.  The upper bound for the magnitude of
  each antidiffusive flux is evaluated using a single sweep of the
  multidimensional FCT limiter at the first outer iteration. This
  semi-implicit limiting strategy makes it possible to enforce the
  positivity constraint in a very robust and efficient manner.
  Moreover, the computation of an intermediate low-order solution can
  be avoided. The nonlinear algebraic systems are solved either by a
  standard defect correction scheme or by means of a discrete Newton
  approach whereby the approximate Jacobian matrix is assembled
  edge-by-edge. Numerical examples are presented for two-dimensional
  benchmark problems discretized by the standard Galerkin FEM combined
  with the Crank-Nicolson time-stepping.