We sketch out the basic properties of three novel exponentially fitted shape functions that generalize to two-dimensional triangular elements the one-dimensional functions used in the well-known Scharfetter-Gummel method. This scheme is widely employed in the finite element approximation of the drift-diffusion equations arising in semiconductor device modelling.
Sacco, R. (1996). Exponentially fitted shape functions for advection-dominated flow problems in two dimensions. Journal of Computational and Applied Mathematics, 67(1), 161–165. https://doi.org/10.1016/0377-0427(95)00149-2