the best-approximation weighted-residuals method for the steady convection-diffusion-reaction problem

in this paper we present an analytical, parameter-free, petrov-galerkin method that gives stable solutions of convection dominated boundary-value problems. we call it the best approximation weighted residuals (bawr) method since it gives the best approximation in the norm induced by the inner-product used to build the weighted-residuals approximation. the method computes the optimal weighting functions by solving suitable adjoint problems. moreover, through a localization technique it becomes computationally efficient without loosing accuracy. the analysis is confirmed by numerical results.