Une nouvelle méthode d'antidiffusion dynamique pour la convection linéaire

Abstract

A new method for the correction of diffusion effects is presented, and a proof of convergence is given. This method needs no test, no restriction on the CFL condition and is active near the extrema of the approximate solution to prevent the decrease of the amplitude of the waves. The main idea is to control the diffusion by a local projection on the first eigenfunction of the Laplace operator, and then to use this term as the source term which is convected by a side equation.