Peculiarities of flux correction in the finite element context are
investigated. Criteria for positivity of the numerical solution are
formulated, and the low-order transport operator is constructed from
the discrete high-order operator by adding modulated dissipation so as
to eliminate negative off-diagonal entries. The corresponding
anti/-diffusive terms can be decomposed into a sum of genuine fluxes
(rather than element contributions) which represent bilateral mass
exchange between individual nodes. Thereby essentially one-dimensional
flux correction tools can be readily applied to multidimensional
problems involving unstructured meshes. The proposed methodology
guarantees mass conservation and makes it possible to design both
explicit and implicit FCT schemes based on a unified limiting
strategy. Numerical results for a number of benchmark problems
illustrate the performance of the algorithm.