The algebraic flux correction (AFC) paradigm is extended
to finite element discretizations with a consistent mass matrix.
It is shown how to render an implicit Galerkin scheme
positivity-preserving and remove excessive artificial diffusion
in regions where the solution is sufficiently smooth. To
this end, the original discrete operators are modified in a
mass-conserving fashion so as to enforce the algebraic
constraints to be satisfied by the numerical solution.
A node-oriented limiting strategy is employed to control the
raw antidiffusive fluxes which consist of a convective
part and a contribution of the consistent mass matrix.
The former offsets the artificial diffusion due to
`upwinding` of the spatial differential operator and
lends itself to an upwind-biased flux limiting. The latter
eliminates the error induced by mass lumping and calls
for the use of a symmetric flux limiter. The concept of
a target flux and a new definition of upper/lower
bounds make it possible to combine the advantages of
algebraic FCT and TVD schemes introduced previously
by the author and his coworkers. Unlike other
high-resolution schemes for unstructured meshes, the new
algorithm reduces to a consistent (high-order) Galerkin
scheme in smooth regions and is designed to provide an
optimal treatment of both stationary and time-dependent
problems. Its performance is illustrated by application
to the linear advection equation for a number of 1D and
2D configurations.