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 H₁ 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 h¹, where J is the number of levels in the multigrid algorithm.