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Spectral discretization of the time-dependent Stokes problem with mixed boundary conditions. (English) Zbl 1479.65005

Summary: In this paper, we consider the time-dependent Stokes problem in a three-dimensional domain with mixed boundary conditions. The discretization relies on spectral methods with respect to the space variables and Euler’s implicit scheme with respect to the time variable, then by the second order BDF method. A detailed numerical analysis leads to a priori error estimates for each numerical scheme.

MSC:

65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
76M15 Boundary element methods applied to problems in fluid mechanics
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