Single collocation point methods for the advection–diffusion equation

This article is offered to honor Professor George F. Pinder. Its technical contents were motivated by an Eulerian–Lagrangian method that was recently proposed by him and his collaborators. Two one-node-collocation algorithms, which may be used to advance that method are presented. Although they are here discussed for 1-D problems only, one of them has already been generalized to problems in several space variables. Thus, this paper essentially generalizes the above mentioned Eulerian–Lagrangian method of Pinder et al. to problems in several dimensions. Also, the results presented in this paper have a wider interest in water resources studies because they apply to advection diffusive transport processes in general. The methodology used to develop the new algorithms is a unified theory of domain decomposition methods (DDM), recently introduced by the authors and which owes much to George F. Pinder. The results reported in the present paper illustrate, by the way, its application and power.