Interpolation Spaces and Optimal Multilevel Preconditioners.
Please always quote using this URN: urn:nbn:de:0297-zib-1285
- This paper throws light on the connection between the optimal condition number estimate for the BPX method and constructive approximation theory. We provide a machinery, which allows to understand the optimality as a consequence of an approximation property and an inverse inequality in $H^{1+\epsilon}$, $\epsilon > 0$. This machinery constructs so-called {\em approximation spaces}, which characterize a certain rate of approximation by finite elements and relates them with interpolation spaces, which characterize a certain smoothness.
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| Author: | Folkmar A. Bornemann |
|---|---|
| Document Type: | ZIB-Report |
| Date of first Publication: | 1993/12/15 |
| Series (Serial Number): | ZIB-Report (SC-93-33) |
| ZIB-Reportnumber: | SC-93-33 |
| Published in: | Appeared in: Contemporary Mathematics Vol. 180 (1994) pp. 3-08 |
