Stability of Discrete Stokes Operators in Fractional Sobolev Spaces
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Using a general approximation setting having the generic properties of finite-elements, we prove uniform boundedness and stability estimates on the discrete Stokes operator in Sobolev spaces with fractional exponents. As an application, we construct approximations for the time-dependent Stokes equations with a source term in L p (0, T; L q (Ω)) and prove uniform estimates on the time derivative and discrete Laplacian of the discrete velocity that are similar to those in Sohr and von Wahl . © 2007 Birkhaueser.
author list (cited authors)
Guermond, J., & Pasciak, J. E.