Methodes d'elements finis pour les problemes de convection-diffusion
Keywords:
modelling, finite elements, convection, diffusion, characteristics, PetrovGalerkin, Taylor-Galerkin, least-squaresAbstract
This paper presents a brief overview of generalized Galerkin methods for the finite element solution of transport problems governed by convection and diffusion. The first part is concerned with steady problems. The emphasis is placed upon the use of Petrov-Galerkin methods to reproduce in the finite element context the upwind effect previously used with success in finite differences. The second part deals with transient problems describing pure convection and, more generally, with situations governed by first-order hyperbolic equations. The methods discussed include techniques making an explicit use of the characteristic curves, Petrov-Galerkin and Taylor-Galerkin methods, as well as least-squares methods.
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