A NORM ESTIMATE FOR THE ADI METHOD FOR NONSYMMETRIC PROBLEMS

We give a norm estimate for the alternating direction implicit method for nonsymmetric elliptic convection-diffusion problems on a rectangul ar domain. We estimate a certain form of the iteration matrix in terms of the coefficients of convective terms and the mesh size. The norm i s shown to be asymptotically of the form (1 - Ch)/(1 + Ch), where C is the same constant as in the symmetric case. We also show that the opt imal size of the parameter is the same as in the symmetric case. As a consequence, we conclude that the convergence behavior is as good as t hat of the symmetric case and does not deteriorate as the size of conv ective terms grows. Numerical experiment shows that ou analysis is sha rp. (C) 1997 Elsevier Science Inc.