Finite Element Methods for Convection Diffusion Equation

Abstract

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It is shown that specially devised exponential elements can be very effective in finite element analysis of convection dominated phenomena.