Non-local pseudo-differential operators

The notion of non-local pseudo-differential operators, as well as their symbols and the operation on holomorphic functions, is established and the invertibility theorem for such operators is proved.     

Modélisation du transport réactif en milieu poreux : schéma itératif associé à une combinaison d'éléments finis discontinus et mixtes-hybridesModelling reactive transport in porous media: iterative scheme and combination of discontinuous and mixed-hybrid finite elements

The sequential iterative approach (SIA) scheme is the most efficient method for modelling reactive transport in porous media with the operator-splitting approach. A combination of finite discontinuous and finite mixed-hybrid elements is a powerful method for solving solute transport in porous media, but the use of this method for SIA scheme induces numerical difficulties. In this paper, a new method is developed to solve reactive transport by using both the SIA scheme and a combination of finite discontinuous and finite mixed elements. The proposed method is tested by modelling a column experiment. To cite this article: J. Carrayrou et al., C. R. Mecanique 331 (2003).