Email this article On Variational Representations of the Constant in the Inf-Sup Condition for the Stokes Problem
- Authors: Repin S.1
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Affiliations:
- St. Petersburg Department of the Steklov, Mathematical Institute, St. Petersburg State Polytechnical University
- Issue: Vol 224, No 3 (2017)
- Pages: 456-467
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/239623
- DOI: https://doi.org/10.1007/s10958-017-3428-y
- ID: 239623
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Abstract
Variational representations of the constant cΩ in the inf-sup condition for the Stokes problem in a bounded Lipschitz domain in ℝd, d ≥ 2, are deduced. For any pair of admissible functions, the respective variational functional provides an upper bound of cΩ and the exact infimum of it is equal to cΩ. Minimization of the functionals over suitable finite dimensional subspaces generates monotonically decreasing sequences of numbers converging to cΩ and, therefore, they can be used for numerical evaluation of the constant.
About the authors
S. Repin
St. Petersburg Department of the Steklov, Mathematical Institute, St. Petersburg State Polytechnical University
Author for correspondence.
Email: repin@pdmi.ras.ru
Russian Federation, St. Petersburg
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