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The accuracy of the fractional step method. (English) Zbl 0953.65061
It is known from the sixties that fractional step methods have significant loss of accuracy in the case of Dirichlet conditions and simple parabolic problems. The authors consider a special variant of such methods for solving initial-boundary value problems associated with nonstationary Navier-Stokes systems with two space variables in the first quadrant. They consider only discretized in time problems. Their main result leads to the conclusion: there are problems with boundary conditions which yield at best only first order approximations.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76M20 Finite difference methods applied to problems in fluid mechanics
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35Q30 Navier-Stokes equations
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