Flux correction tools for finite elements (Q1604478)

The paper introduces a new approach for flux correction in the finite element context for convection-dominated problems. The new aspects concern the technique for the construction of non-oscillatory low-order schemes, the flux-based representation of anti-diffusive terms, and the extension of the FEM-FCT approach to implict time discretization. Several one- and two-dimensional numerical examples for scalar transport problems illustrate the good performance of the schemes in comparison with alternative approaches. Due to the fact that the schemes preserve positivity, strictly conserve mass, and provide sharp resolution of discontinuities, they appear to be very well suited for the considered type of problems. Also, possibilities for an extension of the schemes to incompressible flow problems are briefly discussed.