Multigrid for Locally Refined Meshes

A two-level method for the solution of nite element schemes on locally reened meshes is introduced. The upper bound on the condition number implies, in some cases, mesh-independent convergence, as is veriied numerically for a diiusion problem with discontinuous coeecients. The discontinuity curves are not necessarily aligned with the coarse mesh; indeed, numerical applications with ten levels of local reenement yield a fast convergence for the corresponding ten-level multigrid V-cycle, even when the discontinuities are invisible on most of the coarse meshes.