The paper analyses the numerical performance of preconditioning with Gram m
atrix approximations for the solution of a convection-diffusion equation. T
he convection-diffusion equation is discretized on a rectangular grid by st
andard finite element methods with piecewise linear test and trial function
s. The discrete linear system is solved by two different conjugate gradient
algorithms: CGS and GMRES. The preconditioning with Gram matrix approximat
ions consists of replacing the solving of the equation with the preconditio
ner by a few iterations of an appropriate iterative scheme. Two iterative a
lgorithms are tested: incomplete Cholesky and multigrid. Numerical experime
nts indicate that these preconditioners are efficient at relatively small v
alues of the Reynolds number. (C) 1998 IMACS/Elsevier Science B.V.