Analysis of a class of quasi-monotone and conservative semi-Lagrangian advection schemes

We analyze in the L-infinity-norm a class of semi-Lagrangian advective schemes introduced by the author and A. Staniforth in 1992 to improve the solution produced by numerical models for weather prediction and climate studies that use semi-Lagrangian advective schemes. The new quasimonotone and conservative semi-Lagrangian schemes are L-infinity-stable and converge optimally when the solution is sufficiently smooth.