Monotone Multigrid Methods for Elliptic Variational Inequalities I 1

We derive fast solvers for discrete elliptic variational inequalities of the rst kind (obstacle problems) as resulting from the approximation of related continuous problems by piecewise linear nite elements. Using basic ideas of successive subspace correction, we modify well{known relaxation methods by extending the set of search directions. Extended under-relaxations are called monotone multigrid methods, if they are quasioptimal in a certain sense. By construction, all monotone multigrid methods are globally convergent. We take a closer look at two natural variants, the standard monotone multigrid method and a truncated version. For the considered model problems, the asymptotic convergence rates resulting from the standard approach suuer from insuucient coarse{grid transport, while the truncated monotone multigrid method provides the same eeciency as in the unconstrained case.