Abstract
We analyse multi-grid applied to anisotropic equations within the framework of smoothing and approximation-properties developed by Hack busch. For a model anisotropic equation on a square, we give an up-till-now missing proof of an estimate concerning the approximation property which is essential to show robustness. Furthermore, we show a corresponding estimate for a model anisotropic equation on an L-shaped domain. The existing estimates for the smoothing property are not suitable to prove robustness for either 2-cyclic Gauss-Seidel smoothers or for less regular problems such as our second model equation. For both cases, we give sharper estimates. By combination of our results concerning smoothing- and approximation-properties, robustness of W-cycle multi-grid applied to both our model equations will follow for a number of smoothers.
Original language | English |
---|---|
Pages (from-to) | 373-398 |
Number of pages | 26 |
Journal | Numerische Mathematik |
Volume | 66 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1993 |