| Title:
|
The strengthened C.B.S. inequality constant for second order elliptic partial differential operator and for hierarchical bilinear finite element functions (English) |
| Author:
|
Pultarová, Ivana |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
323-329 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We estimate the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for hierarchical bilinear finite element spaces and elliptic partial differential equations with coefficients corresponding to anisotropy (orthotropy). It is shown that there is a nontrivial universal estimate, which does not depend on anisotropy. Moreover, this estimate is sharp and the same as for hierarchical linear finite element spaces. (English) |
| Keyword:
|
Cauchy-Bunyakowski-Schwarz inequality |
| Keyword:
|
multilevel preconditioning |
| Keyword:
|
elliptic partial differential equation |
| MSC:
|
65N12 |
| MSC:
|
65N22 |
| MSC:
|
65N30 |
| MSC:
|
74S05 |
| idZBL:
|
Zbl 1099.65102 |
| idMR:
|
MR2133733 |
| DOI:
|
10.1007/s10492-005-0020-4 |
| . |
| Date available:
|
2009-09-22T18:22:37Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134609 |
| . |
| Reference:
|
[1] O. Axelsson: A survey of algebraic multilevel iteration (AMLI) methods.BIT Numerical Mathematics 43 (2003), 863–879. Zbl 1049.65139, MR 2058872, 10.1023/B:BITN.0000014564.49281.13 |
| Reference:
|
[2] O. Axelsson, R. Blaheta: Two simple derivations of universal bounds for the C.B.S. inequality constant.Applications of Mathematics (to appear). MR 2032148 |
| Reference:
|
[3] R. Blaheta: GPCG-generalized preconditioned CD method and its use with non-linear and non-symmetric displacement decomposition preconditioners.Numer. Linear Algebra Appl. 9 (2002), 527–550. MR 1934875, 10.1002/nla.295 |
| Reference:
|
[4] O. Axelsson, V. A. Barker: Finite element solution of boundary value problems: Theory and computations.Classics in Appl. Math, SIAM, Philadelphia, 2001. MR 1856818 |
| Reference:
|
[5] J. F. Maitre, F. Mussy: The contraction number of a class of twolevel methods, an exact evaluation for some finite element subspaces and model problem.In: Multigrid Methods, Lecture Notes in Math. 960, W. Hackbusch, U. Trottenberg (eds.), Springer-Verlag, Berlin, 1982, pp. 535–544. |
| . |
