A local L2-error analysis of the streamline diffusion method for nonstationary convection-diffusion systems
نویسندگان
چکیده
— We consider the discretization of linear, nonstationary, convection-dominated, convection-diffusion Systems by the streamline diffusion finite element method and give local error estimâtes in the energy norm for both linear scalar équations in arbitrary dimensions and for Systems in one space dimension. For piecewise linear shape functions in time-space that are continuons in space and discontinuons in time, we obtain optimal local error estimâtes of order O(h ) in those strip régions parallel to the streamline direction in which the exact solution is smooth. Résumé. — Dans cet article nous considérons la discrétisation par la méthode SDFEM (Streamline Diffusion Finite Element Method) d'équations de convection-diffusion linéaires instationnaires à convection dominante. On donne une estimation d'erreur locale dans la norme-énergie pour des équations de convection-diffusion scalaires linéaires instationnaires à convection dominante dans un espace de dimension arbitraire ainsi que pour des systèmes unidimensionnels. On obtient, pour les fonctions de base linéaires par morceaux en temps ainsi qu'en espace (continues en espace et discontinues en temps), une estimation d'erreur locale d'ordre optimal O(h ) dans les bandes parallèles aux caractéristiques où la solution est lisse.
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