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The incompressible Navier-Stokes problem is discretized in time by
the two-step backward differentiation formula.
Error estimates are proved under feasible assumptions on the
regularity of the exact solution avoiding hardly fulfillable
compatibility conditions. Whereas the time-weighted velocity error is
of optimal second order, the time-weighted error in the pressure is
of first order. Suboptimal estimates are shown for a
linearisation. The results cover both the two- and
three-dimensional...
We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.
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