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| - Error estimates for finite element discretizations of the instationary Navier-Stokes equations
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| - In this work we consider the two dimensional instationary Navier-Stokes equations with homogeneous Dirichlet/no-slip boundary conditions. We show error estimates for the fully discrete problem, where a discontinuous Galerkin method in time and inf-sup stable finite elements in space are used. Recently, best approximation type error estimates for the Stokes problem in the L ∞( I; L2(Ω)), L2( I; H1(Ω)) and L2( I; L2(Ω)) norms have been shown. The main result of the present work extends the error estimate in the L∞( I; L2(Ω)) norm to the Navier-Stokes equations, by pursuing an error splitting approach and an appropriate duality argument. In order to discuss the stability of solutions to the discrete primal and dual equations, a specially tailored discrete Gronwall lemma is presented. The techniques developed towards showing the L ∞( I; L2(Ω)) error estimate, also allow us to show best approximation type error estimates in the L2( I; H1(Ω)) and L2( I; L2(Ω)) norms, which complement this work.
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| - © The authors. Published by EDP Sciences, SMAI 2024
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| - The authors. Published by EDP Sciences, SMAI
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