Box method for the convection-diffusion equation based on exponential shape functions

Abstract

We present a derivation of exponential shape functions for the convection diffusion problem. The shape functions are defined for triangular elements and can be regarded as an extension of the one-dimensional Scharfetter-Gummel discretization scheme to two dimensions. The shape function varies exponentially in the direction of the element field vector and linearly in the direction orthogonal to the element drift velocity vector. A conservative discretization scheme is constructed by means of the box method. The resulting element matrix is not necessarily an M-matrix. A measure to stabilize the discretization is briefly outlined.