A positive definite continuous FEM model for advection

This work introduces a continuous and sign-preserving finite element model (FEM) for advection problems. The model is formulated by integrating flux corrected transport technique (FCT) with the characteristic based (CB) FEM. Low order solution for the FCT has the form of element contribution and derives from an upwind monotone scheme with the minimum necessary diffusion for positivity. Selected numerical experiments illustrate the efficacy of the method by comparing results with some successful models, by demonstrating an approximate conservation of the accuracy of original CB algorithm once the complete procedure is operating, and by testing the model for severe time dependent advective flows.