L'approximation quadratique et l'approche Taylor-Galerkin pour Ia modelisation des problemes transitoires d' advection -diffusion - Khelifa, Ali; Robert, Jean-Loop; Ouellet, Yvon (European Journal of Computational Mechanics, 1995)
This paper presents a numerical study of the behaviour of a model based on quadratic finite element approximation for transient advection-diffusion problem modelling. This model is based on a classical splitting technique, the advection-diffusion equation being split in time. The advection part is computed by a &-weighting Taylor-Galerkin approach. As to the diffusion equation, it's discretized by a standard &-weighting Galerkin scheme. For these two phases and based on Fourier method, an error analysis is proposed using quadratics elements. Results of this analysis show interesting investigations on the behaviour of numerical schemes based on high approximations. These investigations are confirmed by some representative numerical examples in one and two dimensions.