| Abstract: | The purpose of this paper is to present a new algorithm for the resolution of both interior and boundary layers present in the convection–diffusion equation in laminar regimes, based on the formulation of a family of polynomial– exponential elements. We have carried out an adaptation of the standard variational methods (finite element method and spectral element method), obtaining an algorithm which supplies non-oscillatory and accurate solutions. The algorithm consists of generating a coupled grid of polynomial standard elements and polynomial–exponential elements. The latter are able to represent the high gradients of the solution, while the standard elements represent the solution in the areas of smooth variation. |
