Steady-state diffusion-advection by exponential finite elements

Conventional finite-element solutions of the diffusion-advection equation exhibit numerical oscillations around the exact solution in the presence of strong advective transport. Stabilized methods modifying the standard Galerkin statement of the equation are usually used to remove oscillations and improve the speed of convergence of the method. This paper proposes an alternative approach, based on an unmodified Galerkin statement using a special eight-noded finite element whose interpolation functions vary exponentially, rather than polynomially, yielding a better approximation of the solution of the differential equation. In one-dimensional problems with specified concentration or flux at the inlet, the method increases the element Péclet number limit from 1 to 150. In two-dimensional problems, a significant improvement in accuracy relative to conventional polynomial elements is achieved. The method is particularly suitable for the h-adaptive schemes and can be easily incorporated into existing finite-element software through a minimal modification of their element libraries. © 2006 ASCE.