A new approach to flux correction for finite elements is presented.
The low-order transport operator is constructed from the discrete
high-order operator by elimination of negative off-diagonal entries,
so as to enforce the M-matrix property. The corresponding antidiffusive
terms can be decomposed into a sum of internodal fluxes (rather
than element contributions). Thereby essentially one-dimensional
flux correction tools can be applied on unstructured meshes.
The proposed algorithm guarantees mass conservation and makes
it possible to design both explicit and implicit FEM-FCT schemes
based on a unified limiting procedure.