By means of the integral version of vortex equation, the technique of Green's function, and the vorticity-to-velocity map, a new kind of interval methods for solving the initial-periodic boundary value problem of two-dimensional incompressible Navier–Stokes equation is introduced, which consists of both an approximate scheme and a set of pointwise intervals covering the exact solution. The convergence theorem corresponding to the scheme is proved, and the order of error width for the two-sided bounds is also considered. Finally, a simple numerical example illustrates our corroboration. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1368–1396, 2014
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