Details
| Original language | English |
|---|---|
| Pages (from-to) | 1003-1022 |
| Number of pages | 20 |
| Journal | Mathematical Modelling and Numerical Analysis |
| Volume | 34 |
| Issue number | 5 |
| Publication status | Published - 2000 |
| Externally published | Yes |
Abstract
Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate a posteriori error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator. As an alternative, we introduce an adaptive variant of Uzawa's algorithm and prove its convergence. Secondly, we derive explicit criteria for adaptively refined wavelet spaces in order to fulfill the Ladyshenskaja-Babuška Brezzi (LBB) condition and to be fully equilibrated.
Keywords
- A posteriori error estimates, Adaptive schemes, Multiscale methods, Saddle point problems, Uzawa's algorithm, Wavelets
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Mathematical Modelling and Numerical Analysis, Vol. 34, No. 5, 2000, p. 1003-1022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Adaptive wavelet methods for saddle point problems
AU - Dahlke, Stephan
AU - Hochmuth, Reinhard
AU - Urban, Karsten
PY - 2000
Y1 - 2000
N2 - Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate a posteriori error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator. As an alternative, we introduce an adaptive variant of Uzawa's algorithm and prove its convergence. Secondly, we derive explicit criteria for adaptively refined wavelet spaces in order to fulfill the Ladyshenskaja-Babuška Brezzi (LBB) condition and to be fully equilibrated.
AB - Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate a posteriori error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator. As an alternative, we introduce an adaptive variant of Uzawa's algorithm and prove its convergence. Secondly, we derive explicit criteria for adaptively refined wavelet spaces in order to fulfill the Ladyshenskaja-Babuška Brezzi (LBB) condition and to be fully equilibrated.
KW - A posteriori error estimates
KW - Adaptive schemes
KW - Multiscale methods
KW - Saddle point problems
KW - Uzawa's algorithm
KW - Wavelets
UR - http://www.scopus.com/inward/record.url?scp=0034356805&partnerID=8YFLogxK
U2 - 10.1051/m2an:2000113
DO - 10.1051/m2an:2000113
M3 - Article
AN - SCOPUS:0034356805
VL - 34
SP - 1003
EP - 1022
JO - Mathematical Modelling and Numerical Analysis
JF - Mathematical Modelling and Numerical Analysis
SN - 0764-583X
IS - 5
ER -