Abstract
Multigrid methods applied to standard linear finite element discretizations of linear elliptic boundary value problems in two dimensions are considered. In the multigrid method, damped Jacobi or damped Gauss-Seidel is used as a smoother. It is proven that the two-grid method with v pre-smoothing interations has a contraction number with respect to the maximum norm that is (asymptotically) bounded by Cv-1/2|lnhk|2, with hk a suitable mesh size parameter. Moreover, it is shown that this bound is sharp in the sense that a factor |ln hk| is necessary.
| Original language | English |
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| Pages (from-to) | 378-392 |
| Number of pages | 15 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 31 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1994 |