Multigrid for Locally Refined Meshes

Yair Shapira
Los Alamos National Laboratory
Mail Stop B-256
Los Alamos, NM 87545


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.

Contributed December 2, 1996.