Remarks on the Lagrangian stucture of the Eikonal Equation and its impact on Eulerian numerics

Abstract : We make use of the {\em Lagangian structure} of the Eikonal equation obtained by considering its gradient to \begin{enumerate} \item observe a superconvergence phenomena on the Rouy-Tourin first order algorithm . \item propose a second order pure upwind extension of the Rouy Tourin algorithm. \end{enumerate} We also discuss the exension of this second order algorithm to the Transport equation.