Two-level Picard and modified Picard methods for the Navier-Stokes equations
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 \(O(h^2_0)\) 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 \(h\to 0\). Further, the fine mesh solution satisfies a quasi-optimal error bound.
scientific article; zbMATH DE number 761791
scientific article