Multigrid for Locally Refined Meshes

                                 Yair Shapira

          Computer Science Department, Technion, Haifa 32000, Israel
                    Now at Los Alamos National Laboratory
                        MS B-256, Los Alamos NM 87545
                           e-mail: yairs@lanl.gov.

                                   Abstract

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