Comparison between the different projections of the interior fields obtained using Tóth & Roe’s operator (blue) and the nonlinear operator here derived (red), from the same exterior fluxes (black) and for a cubic cell. Each panel corresponds to a slice of a coarse cell, for which the indices of the fine cells are given at the upper left (cf. Fig. 3). The direction of the original flux is better preserved by the nonlinear operator (cf. right panels), where a component in the y-direction that was not originally present appears for the Tóth & Roe operator. The field interpolated using the nonlinear operator is exactly zero for cells with j = −1. For clarity, vectors in the lower left panel are represented with a double size.