Abstract.
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 [20].
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Communicated by G. P. Galdi
On long leave from LIMSI (CNRS-UPR 3251), BP 133, 91403, Orsay, France.
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Guermond, JL., Pasciak, J.E. Stability of Discrete Stokes Operators in Fractional Sobolev Spaces. J. math. fluid mech. 10, 588–610 (2008). https://doi.org/10.1007/s00021-007-0244-z
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DOI: https://doi.org/10.1007/s00021-007-0244-z