FEM‐FCT: Combining unstructured grids with high resolution

Abstract We present the extension of flux‐corrected transport (FCT) schemes to unstructured grids. The spatial discretization is performed via finite elements. In particular, we have chosen triangular elements in two dimensions. The limiting procedure is based on Zalesak's extension to more than one dimension of the FCT schemes developed by Boris and Book. The resulting scheme, FEM‐FCT, is capable of resolving moving and stationary shocks within two elements, and several examples are given that demonstrate the accuracy attainable, even for complicated geometries.