کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4641528 | 1341311 | 2009 | 13 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Schur complements on Hilbert spaces and saddle point systems Schur complements on Hilbert spaces and saddle point systems](/preview/png/4641528.png)
For any continuous bilinear form defined on a pair of Hilbert spaces satisfying the compatibility Ladyshenskaya–Babušca–Brezzi condition, symmetric Schur complement operators can be defined on each of the two Hilbert spaces. In this paper, we find bounds for the spectrum of the Schur operators only in terms of the compatibility and continuity constants. In light of the new spectral results for the Schur complements, we review the classical Babušca–Brezzi theory, find sharp stability estimates, and improve a convergence result for the inexact Uzawa algorithm. We prove that for any symmetric saddle point problem, the inexact Uzawa algorithm converges, provided that the inexact process for inverting the residual at each step has the relative error smaller than 1/3. As a consequence, we provide a new type of algorithm for discretizing saddle point problems, which combines the inexact Uzawa iterations with standard a posteriori error analysis and does not require the discrete stability conditions.
Journal: Journal of Computational and Applied Mathematics - Volume 225, Issue 2, 15 March 2009, Pages 581–593