Un Método de Petrov-Galerkin para las Ecuaciones de Convección-Difusión

Abstract

Galerkin methods applied to diffusion - convection problems produce inaccuracies and oscillations. Petrov-Galerkin methods have been introduced by several authors to eliminate these problems. In this work we propose to select an appropiate trial space for a given test space based on a posteriori error analysis of the finite element aproximation. Thus, we obtain a posteriori error estimate associated with it. Moreover, we show that the quasi - optimability may be recovered by using these spaces.
Based on the symetrization concept introduced by Barret-Morton (1984), we found a general error bound. We show that for the diffusion-convection problem in one dimension the Petrov-Galerkin formulation gives the same algebraic system of equations that the formulation known as the control volume based on finite element method (CVFEM) introduced by S. Patankar (1980).