Characterization of discrete commutative filters

Previous work by the authors (J. Comp. Phys., 187: 197-211, 2003) derived and analyzed discrete commutative filters. On uniform unbounded grids, the discrete commutation error was shown numerically to be of the order of the machine precision. On non-uniform and bounded grids, numerical experiments confirmed the theoretical prediction that the discrete commutation error depends on both the order of accuracy of the discrete filter operator and the order of accuracy of the spatial discretization. For discrete filters to be of genuine practical value, their widths must be prescribed. This leads to the problem of characterization of discrete filters, that is, how to express their width in terms of quantities such as the local grid spacing and filter moments. The presentation will describe ongoing investigations into the characterization of discrete filters.