期刊
NUMERISCHE MATHEMATIK
卷 120, 期 1, 页码 1-34出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00211-011-0401-4
关键词
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资金
- NSF [DMS-0505454, DMS-0811272, MS-0505454, DMS-0807811, DMS-0609727, DMS 0915153, NSFC-10528102]
- UC Irvine Academic Senate Council on Research, Computing and Libraries (CORCL)
- Alexander von Humboldt Research Award
- Direct For Mathematical & Physical Scien [0811272] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [0811272] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0807811] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [915153] Funding Source: National Science Foundation
We design and analyze optimal additive and multiplicative multilevel methods for solving H (1) problems on graded grids obtained by bisection. We deal with economical local smoothers: after a global smoothing in the finest mesh, local smoothing for each added node during the refinement needs to be performed only for three vertices - the new vertex and its two parent vertices. We show that our methods lead to optimal complexity for any dimensions and polynomial degree. The theory hinges on a new decomposition of bisection grids in any dimension, which is of independent interest and yields a corresponding decomposition of spaces. We use the latter to bridge the gap between graded and quasi-uniform grids, for which the multilevel theory is well-established.
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