  Efficient transport algorithms are essential to the numerical resolution of
incompressible fluid flow problems. Semi-Lagrangian methods are widely used in
grid based methods to achieve this aim. The accuracy of the interpolation
strategy then determines the properties of the scheme. We introduce a simple
multi-stage procedure which can easily be used to increase the order of
accuracy of a code based on multi-linear interpolations. This approach is an
extension of a corrective algorithm introduced by Dupont \& Liu (2003, 2007).
This multi-stage procedure can be easily implemented in existing parallel codes
using a domain decomposition strategy, as the communications pattern is
identical to that of the multi-linear scheme. We show how a combination of a
forward and backward error correction can provide a third-order accurate
scheme, thus significantly reducing diffusive effects while retaining a
non-dispersive leading error term.
