Abstract
In this paper, we prove two-sided bounds on the convergence rate of a standard two-level subspace correction method. We then apply these estimates to show that a two-level method with point-wise smoother for variational problem in H0 (curl) does not have optimal convergence rate. This result justifies the conclusion, observed numerically and reported in the literature, that a point relaxation as a smoother does not lead to an optimal multigrid method. In fact, we show that for such problems using a well-conditioned smoother will always lead to a method that is not optimal.
Original language | English (US) |
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Pages (from-to) | 439-454 |
Number of pages | 16 |
Journal | Numerical Linear Algebra with Applications |
Volume | 15 |
Issue number | 5 SPEC. ISS. |
DOIs | |
State | Published - Jun 1 2008 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Applied Mathematics