Adaptive wavelet methods for saddle point problems

authored by: Stephan Dahlke, Reinhard Hochmuth, Karsten Urban
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.
External Organisation(s): RWTH Aachen University
Freie Universität Berlin (FU Berlin)
Type: Article
Journal: Mathematical Modelling and Numerical Analysis
Volume: 34
Pages: 1003-1022
No. of pages: 20
ISSN: 0764-583X
Publication date: 2000
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Analysis, Numerical Analysis, Modelling and Simulation, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1051/m2an:2000113 (Access: Open)
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