Details
| Original language | English |
|---|---|
| Pages (from-to) | 789-806 |
| Number of pages | 18 |
| Journal | Numerical Functional Analysis and Optimization |
| Volume | 19 |
| Issue number | 7-8 |
| Publication status | Published - 1998 |
Abstract
Stability for discretizations of saddle point problems is typically the result of satisfying the discrete Babuška-Brezzi condition. As a consequence a number of natural discretizations are ruled out and some effort is required to provide stable ones. Therefore ideas for circumventing the Babuška-Brezzi condition are interesting. Here an ansatz presented in a series of papers by Hughes et al. is described and investigated in the framework of multiscale discretizations. In particular discretizations for appending boundary conditions by Lagrange multipliers and the stationary Stokes problem are considered. Sufficient conditions for their stability are given and diagonal preconditioners which give uniformly bounded condition numbers are proposed.
Keywords
- Condition numbers, Multiscale methods, Saddle point problems, Stability
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Computer Science(all)
- Signal Processing
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Control and Optimization
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In: Numerical Functional Analysis and Optimization, Vol. 19, No. 7-8, 1998, p. 789-806.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stable Multiscale Discretizations for Saddle Point Problems and Preconditioning
AU - Hochmuth, Reinhard
PY - 1998
Y1 - 1998
N2 - Stability for discretizations of saddle point problems is typically the result of satisfying the discrete Babuška-Brezzi condition. As a consequence a number of natural discretizations are ruled out and some effort is required to provide stable ones. Therefore ideas for circumventing the Babuška-Brezzi condition are interesting. Here an ansatz presented in a series of papers by Hughes et al. is described and investigated in the framework of multiscale discretizations. In particular discretizations for appending boundary conditions by Lagrange multipliers and the stationary Stokes problem are considered. Sufficient conditions for their stability are given and diagonal preconditioners which give uniformly bounded condition numbers are proposed.
AB - Stability for discretizations of saddle point problems is typically the result of satisfying the discrete Babuška-Brezzi condition. As a consequence a number of natural discretizations are ruled out and some effort is required to provide stable ones. Therefore ideas for circumventing the Babuška-Brezzi condition are interesting. Here an ansatz presented in a series of papers by Hughes et al. is described and investigated in the framework of multiscale discretizations. In particular discretizations for appending boundary conditions by Lagrange multipliers and the stationary Stokes problem are considered. Sufficient conditions for their stability are given and diagonal preconditioners which give uniformly bounded condition numbers are proposed.
KW - Condition numbers
KW - Multiscale methods
KW - Saddle point problems
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=0032164744&partnerID=8YFLogxK
U2 - 10.1080/01630569808816859
DO - 10.1080/01630569808816859
M3 - Article
AN - SCOPUS:0032164744
VL - 19
SP - 789
EP - 806
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
SN - 0163-0563
IS - 7-8
ER -