✦ LIBER ✦

Stabilizing the Hierarchical Basis by Approximate Wavelets, I: Theory

✍ Scribed by Panayot S. Vassilevski; Junping Wang

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 186 KB
Volume: 4
Category: Article
ISSN: 1070-5325
DOI: 10.1002/(sici)1099-1506(199703/04)4:2<103::aid-nla101>3.0.co;2-j

No coin nor oath required. For personal study only.

✦ Synopsis

This paper proposes a stabilization of the classical hierarchical basis (HB) method by modifying the HB functions using some computationally feasible approximate L 2 -projections onto finite element spaces of relatively coarse levels. The corresponding multilevel additive and multiplicative algorithms give spectrally equivalent preconditioners, and one action of such a preconditioner is of optimal order computationally. The results are regularity-free for the continuous problem (second order elliptic) and can be applied to problems with rough coefficients and local refinement.