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

Summary.   We analyze in the 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 quasi-monotone and conservative semi-Lagrangian schemes are stable and converge optimally when the solution is sufficiently smooth. Received May 17, 1999 / Revised version received November 22, 1999 / Published online August 24, 2000