Preconditioning by approximations of the Gram matrix for convection-diffusion equations

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.