Stable Multiscale Discretizations for Saddle Point Problems and Preconditioning

authored by

Reinhard Hochmuth

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.

Organisation(s)

Institute of the Teaching of Mathematics and Physics

External Organisation(s)

Freie Universität Berlin (FU Berlin)

Type

Article

Journal

Numerical Functional Analysis and Optimization

Volume

19

Pages

789-806

No. of pages

18

ISSN

0163-0563

Publication date

1998

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Analysis, Signal Processing, Computer Science Applications, Control and Optimization

Electronic version(s)

https://doi.org/10.1080/01630569808816859 (Access: Unknown)