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An automatic adaptive refinement technique has been coupled to the multigrid approach to produce an efficient and stable solution strategy for solving the steady-state incompressible Navier-Stokes equations. Solutions have been obtained for the driven cavity and flow over a backward-facing step, for Reynolds numbers up to 5000 and 800, respectively. The refinement criterion is based on the local truncation error. The solution error is monitored and automatic refinement can continue until it isdoi:10.1016/0021-9991(89)90037-5 fatcat:dgtennownjgpfbrhhln63pi234