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 sche mes introduced by the author and A. Staniforth in 1992 to improve the solut ion produced by numerical models for weather prediction and climate studies that use semi-Lagrangian advective schemes. The new quasimonotone and cons ervative semi-Lagrangian schemes are L-infinity-stable and converge optimal ly when the solution is sufficiently smooth.