STABILIZING THE HIERARCHICAL BASIS BY APPROXIMATE WAVELETS .1. THEORY

This paper proposes a stabilization of the classical hierarchical basi s (HB) method by modifying the HB functions using some computationally feasible approximate L-2-projections onto finite element spaces of re latively coarse levels. The corresponding multilevel additive and mult iplicative algorithms give spectrally equivalent preconditioners, and one action of such a preconditioner is of optimal order computationall y. The results are regularity-free for the continuous problem (second order elliptic) and can be applied to problems with rough coefficients and local refinement. (C) 1997 by John Wiley & Sons, Ltd.