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We prove stability of the finite element Stokes projection in the product space W1,∞(Ω)×L∞(Ω), i.e., the maximum norm of the discrete velocity gradient and discrete pressure are bounded by the sum of the corresponding exact counterparts, independently of the mesh-size. The proof relies on weighted L2 estimates for regularized Green's functions associated with the Stokes problem and on a weighted inf–sup...
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