The algebraic flux correction (AFC) paradigm is extended
to finite element discretizations with a consistent mass matrix.
A nonoscillatory low-order scheme is constructed by resorting
to mass lumping and conservative elimination of negative
off-diagonal coefficients from the discrete transport operator.
In order to recover the high accuracy of the original
Galerkin scheme, a limited amount of compensating
antidiffusion is added in regions where the solution is
sufficiently smooth. The raw antidiffusive fluxes, which
include a contribution of the consistent mass matrix, are
limited node-by-node so as to satisfy algebraic constraints
imposed on the discrete solution. The proposed limiting
strategy combines the advantages of multidimensional
FEM-FCT and FEM-TVD schemes introduced previously. Its
performance is illustrated by application to scalar
convection problems in 1D and 2D.