Error estimates for Lagrangian flow field representations

Computing power outpaces I/O bandwidth in modern high performance computers, which leads to temporal sparsity in flow simulation data. Experiments show that Lagrangian flow representations (where pathlines are retrieved from short-time flow maps using interpolation and concatenation) outperform their Eulerian counterparts in advection tasks under these circumstances. Inspired by these results, we present the theoretical estimate of the Lagrangian error for individual pathlines, depending on the choice of temporal as well as spatial resolution. In-situ, this measure can be used to steer the output resolution and post-hoc, it can be used to visualize the uncertainty of the pathlines. To validate our theoretical bounds, we evaluate the measured and the estimated error for several example flow fields.