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Two-level Picard and modified Picard methods for the Navier-Stokes equations. (English) Zbl 0828.76017
Iterative methods of Picard type for the Navier-Stokes equations are known to converge only for quite small Reynolds numbers. However, we study methods involving just one such iteration at general Reynolds numbers. For the initial approximation a coarse mesh of width h 0 is used. The corrected approximation is computed by just one Picard or modified Picard step on a fine mesh of width h 1 . For example, h 1 may be of order O(h 0 2 ) when linear velocity elements are used. The resulting method requires the solution of a (small) system of nonlinear equations on the coarse mesh and only one (larger) linear system on the fine mesh. This two-level Picard method is proven to converge for fixed Reynolds number as h0. Further, the fine mesh solution satisfies a quasi-optimal error bound.
76D05Navier-Stokes equations (fluid dynamics)
76M10Finite element methods (fluid mechanics)
65H10Systems of nonlinear equations (numerical methods)