A new iterative algorithm for the solution of the three‐dimensional Navier–Stokes equations by the finite element method is presented. This algorithm is based on a combination of the Uzawa and the Arrow–Hurwicz algorithms and uses a preconditioning technique to enhance convergence. Numerical tests are presented for the cubic cavity problem with two elements, namely the linear brick Q 1 −P 0 and the enriched linear brick Q 1 + − P 1 . It is shown that the proposed methodology is optimal with the enriched element and that the CPU time varies as NEQ 1·44 , where NEQ is the number of equations.
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Robichaud et al. (1990) studied this question.
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