Flux correction tools for finite elements

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 antidiffusive 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.