Georges Djoumna , Roger Pierre and Daniel LeRoux
gdjoumna@mat.ulaval.ca 

High order finite element interpolating schemes for ocean modelling.

We propose to solve the non linear shallow-water equations
using the finite-element and the semi-Lagrangian methods. A
class of C1 finite element interpolating schemes is used and
two semi-Lagrangian methods are considered: tracking the feet
of the characteristics from 1) the interpolation and 2) the
integration nodes.
We first present some analytical results quantifying the amount
of artificial viscosity induced by the two methods. For the
second approach, the numerical stability is considered. We then
introduces the C1 interpolating schemes: the Hsieh-Clough-Tocher
family (reduced and complete). The performance of our approach
is tested using two numerical tests: the propagation of a soliton
and the evolution of an eddy in an ocean basin. The model is
compared to existing methods both in terms of accuracy and
computational cost.