Multigrid for Refined Triangle Meshes

                                Yair Shapira *

                                   Abstract

A two-level preconditioning method for the solution of (locally) refined
finite element schemes using triangle meshes is introduced.  In the isotropic
SPD case, it is shown that the condition number of the preconditioned
stiffness matrix is bounded uniformly for all sufflciently regular
triangulations.  This is also verified numerically for an isotropic diffusion
problem with highly discontinuous coefflcients.

* 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.