Summary
Having in our mind the general rule from numerical mathematics: “more regular solutions allow approximations of a higher convergence rate also in stronger norms” first of all we point out the optimum regularity of a Navier-Stokes solution at its initial time. Then by means of our result we state H 2-convergence of a sequence of linearizations and of Rothe’s scheme to the Navier-Stokes initial-boundary value problem. By a numerical realization of this general approach, W. Borchers and our Paderborn group have calculated 3-dimensional viscous incompressible flows past a sphere (without symmetry assumptions) at Reynolds numbers 20000 [5].
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Rautmann, R. (1994). Optimum regularity of Navier-Stokes solutions at time t = 0 and applications. In: Schnerr, G.H., Bohning, R., Frank, W., Bühler, K. (eds) Fluid- and Gasdynamics. Acta Mechanica, vol 4. Springer, Vienna. https://doi.org/10.1007/978-3-7091-9310-5_41
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