A norm estimate for the ADI method for nonsymmetric problems (Q1372964)

The author considers elliptic convection-diffusion problems on a rectangle. The norm of the iteration matrix resulting from an alternating direction implicit (ADI) method is estimated. It is shown that the norm is asymptotically of the form \((1-ch)/(1+ch)\). Furthermore, it is proved that the asymptotic convergence factor is as good as in the symmetric case with the same optimal choice of the iteration parameters. Consequently, the convergence is unaffected by the presence of nonsymmetric terms. Numerical experiments confirm the theoretical results.