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This article presents a study on the function of the Péclet number that appears in the upwind function of the GLS, CAU and SAUPG methods, using linear and quadratic triangular elements, as well as bilinear and quadratic quadrilateral elements. The numerical experiments indicate that in the case of elements with faces on the “outflow boundary”, the upwind function is strongly dependent on the geometry and on the degree of the interpolate polynomial. A new function of the Péclet number is therefore proposed, to take these effects into consideration, creating a new method of stabilization for higher order elements. This new stabilized and accurate finite element formulation for convection dominated problems, based on the idea of the SAUPG method, uses the GLS formulation as starting point.