Convergence estimates of multilevel additive and multiplicative algorithms for non-symmetric and indefinite problems

New uniform estimates for multigrid algorithms are established for certain non-symmetric indefinite problems. In particular, we are concerned with the simple additive algorithm and multigrid (V(1, 0)-cycle) algorithms given in [5]. We prove, without full elliptic regularity assumption, that these algorithms have uniform reduction per iteration, independent of the finest mesh size and number of refinement levels, provided that the coarsest mesh size is sufficiently small.