The convergence of the cascadic conjugate-gradient method applied to elliptic problems in domains with re-entrant corners

We study the convergence properties of the cascadic conjugate-gradient meth od (CCG-method), which can be considered as a multilevel method without coa rse-grid correction. Nevertheless, the CCG-method converges with a rate tha t is independent of the number of unknowns and the number of grid levels. W e prove this property for two-dimensional elliptic second-order Dirichlet p roblems in a polygonal domain with an interior angle greater than pi. For p iecewise linear finite elements we construct special nested triangulations that satisfy the conditions of a "triangulation of type (h, gamma, L)" in t he sense of I. Babuska, R. B. Kellogg and J. Pitkaranta. In this way we can guarantee both the same order of accuracy in the energy norm of the discre te solution and the same convergence rate of the CCG-method as in the case of quasiuniform triangulations of a convex polygonal domain.