Convergence of multigrid methods for nonsymmetric, indefinite problems

摘要

A convergence theory is developed for multigrid methods for nonsymmetric, indefinite problems in a variational setting. We prove fast convergence with any bounded positive number of smoothing steps for V- and W-cycles under discrete analogues of the H1 + α regularity assumption. The lower-order nonsymmetric terms are treated as perturbations. In addition, we analyze a wide class of smoothers and get estimates of contraction numbers for multigrid methods with these smoothers.