Best-approximation error estimates are extended from the Stokes problem to the instationary Navier-Stokes equations in the L^∞(I;L²(Ω)), L²(I;H¹(Ω)), and L²(I;L²(Ω)) norms via error splitting and a tailored discrete Gronwall lemma.
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Establishes well-posedness of an optimal control problem for instationary Navier-Stokes with pressure boundary control by means of a suitable tracking term and derives new L2(I;H2) regularity for the associated Stokes problem with mixed boundary conditions.
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Error estimates for finite element discretizations of the instationary Navier-Stokes equations
Best-approximation error estimates are extended from the Stokes problem to the instationary Navier-Stokes equations in the L^∞(I;L²(Ω)), L²(I;H¹(Ω)), and L²(I;L²(Ω)) norms via error splitting and a tailored discrete Gronwall lemma.
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Optimal Control of the Navier-Stokes equations via Pressure Boundary Conditions
Establishes well-posedness of an optimal control problem for instationary Navier-Stokes with pressure boundary control by means of a suitable tracking term and derives new L2(I;H2) regularity for the associated Stokes problem with mixed boundary conditions.