Multigrid for Refined Triangle Meshes

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


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.

Contributed August 29, 1996.