Performance of LCD iterative method in the finite element and finite difference solution of convection–diffusion equations

In this work, we evaluate the performance of the left conjugate direction method (LCD) for the solution of non-symmetric systems of linear equations arising from finite element and finite difference discretizations of the convection–diffusion equation. We extend the LCD algorithm proposed by Dai and Yuan (Int. J. Numer. Meth. Engng 2004; 60:1383–1399) to accommodate restarts. Our discussion considers comparison studies between the computational efficiency of the GMRES and LCD methods and some issues related to the choice of the forcing term in the inexact Newton method. Copyright © 2005 John Wiley & Sons, Ltd.