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In this article we study the operator which appears in the Usawa algorithm classically used in the solution of the Stokes problem, in particular when finite element discretisations are used (see [1],[11]). We call this operator the Usawa operator. We consider S (and-Δ) as a self–adojoint operator in L2Ωfor several domains Ωwith a particular emphasis on the channel flow problem; in this case we determine all the eigenvalues of S and give a precise description of S.
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