Convergence analysis of multigrid algorithms for nonselfadjoint and indefinite elliptic problems

A convergence estimate is established for “nonsymmetric” multigrid algorithms for finite element methods for nonselfadjoint and indefinite elliptic problems. It is shown, without further regularity assumption beyond $H_1 $ necessary to define the weak form, that the V-cycle algorithm converges with rate bounded by $1 - (CJ)^{ - 1} $ for sufficiently small coarse mesh size $h^1 $, where J is the number of levels in the multigrid algorithm.