Daniel Y. Le Roux
Professeur Agrégé - Associate Professor
Département de mathématiques et de statistique
Université Laval, cité universitaire
Québec (QC), G1K 7P4
e-mail   : dleroux@mat.ulaval.ca
tel      : 1 (418) 656-7348

The numerical approximation of the shallow-water equations is a delicate
problem and many issues regarding their spatial discretization are still
open questions. Our purpose is to bring some light on some of them. We
first present new dispersion analysis results concerning the propagation
of Rossby waves in ocean modelling for several mixed finite element
formulations. The influence of the mass lumping procedure will be
analysed and discussed. Some strange and unexpected oscillating results
will be explained. We then propose to improve the quality of the solutions
by trying to adapt the mesh according to the deficiencies of the numerical
methods, shown by analytical studies, a kind of a priori adaptation. Some
interesting results are obtained for the P1NC-P1 pair and RT0 element.
Finally, we prove that the P1NC-P1 pair satisfies the so-called LLB condition.